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会议征稿:第四届计算机、物联网与控制工程国际学术会议(CITCE 2024)
Call for papers: 2024 4th International Conference on Computer, Internet of Things and Control Engineering (CITCE 2024) will be held on November 1-3, 2024 in Wuhan, China as a hybrid meeting.
Conference website(English):https://ais.cn/u/IJfQVv
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大会时间:2024年11月1-3日
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第四届计算机、物联网与控制工程国际学术会议(CITCE 2024)将于2024年11月1-3日在中国-武汉召开。CITCE 2024将围绕计算机、物联网与控制工程的最新研究领域,为来自国内外高等院校、科学研究所、企事业单位的专家、教授、学者、工程师等提供一个分享专业经验、扩大专业网络、展示研究成果的国际平台,以期推动该领域理论、技术在高校和企业的发展和应用,也为参会者建立业务或研究上的联系以及寻找未来事业上的全球合作伙伴。大会诚邀国内外高校、科研机构专家、学者,企业界人士及其他相关人员参会交流。
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For more details about the conference, please visit the official website of the conference: https://ais.cn/u/IJfQVv
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S. Hasan Saeed treated wrote on Automatic Control Systems (with MATLAB programs) and one of his books has Chapter 12 as Robust Control Systems. If you have the book, kindly take snap shot of chapter 12 only and send to jocianvef2004@gmail.com, please. I am dare in need of his explanation in that topic.
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Modern Control Engineering
Book by Katsuhiko Ogata
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2023 3nd International Conference on Electrical Engineering and Control Science(IC2ECS 2023)is to be held in Hangzhou, China during December 29-31, 2023.
The topics of interest for submission include, but are not limited to:
1. Electrical Engineering
Embedded systems
Optimal, Robust Control
...
2. Control Science
Power system optimization
Power distribution automation systems
...
For More Details please visit:
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Please, how much is the article processing charge?
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What kind of nonlinear strategies can be utilized as the best controller in the condition that there is no information about the model of the system?
Consider that the model of the nonlinear system is unavailable and there is no information about it, regardless of estimating the model, which means that the model is very complicated and we can not estimate it properly. In the mentioned situation, what kind of controller could have better performance in the same conditions?
For instance, robust controllers such as sliding mode controllers have good performance.
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Hi Mohammad Javad Mirzaei for estimation of state of a nonlinear system you can use High Gain Observer. If you know some of the states or the out of the system you can apply High Gain Observer. For linear System we can use linear observer or Kalman filter but in nonlinear case these two are mostly failed. So, its better to use high gain observer.
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Dear Colleagues ; I am interested in studying adaptive control and i need to answers some questions they are as follows:
*Who which gives the good performance between a direct or indirect MRAC?
*Can i apply the MRAC if the system has disturbance ?
*Is MRAC robust control ?
*What is a relationship between the a parameter estimation of the system and MRAC?.
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*Who which gives the good performance between a direct or indirect MRAC?
Direct adaptive control (DAC) schemes perform better. Theoretically the stability proofs of DAC closed-loop system are less complex. These loop are robust to the disturbances.
*Can i apply the MRAC if the system has disturbance ?
Yes.
*Is MRAC robust control ?
You can develop robust adaptive controllers.
*What is a relationship between the a parameter estimation of the system and MRAC?. When you directly estimate the parameters of the controller, such loop are known as direct adaptive control schemes. When the controller parameters are designed based of the plant parameter estimation, schemes is called indirect.
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hello dear colleagues
I was working on a problem where I decide to merge sliding mode controller with homogeneous one. I was planning to define the sliding manifold based on homogeneous system of integrators.
Has anybody tried it out? are there any advantages?
best regards
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You are welcome. In my opinion, I think such papers have not yet been contributed, because the topic is brand-new and needs more research contributions to be recently developed. You may be the one who contributes the first paper on this field and with respect to the finite-time stabilization, compare such controllers together, in terms of advantages and disadvantages.
Regards
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I'm looking to detect senescence in Zebrafish embryo and I need a robust control positive (and negative).
Kishi Shuji suggest BHP but exists a better control?
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Does it work
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In controller design for mixed H2 - Hinf performance, ||W1(s)S(s)||inf<1 and ||W2(s)T(s)||inf<1 are to be satisfied simultaneously. The question is how to obtain the weight W1(s)?
Is there any generalized way to obtain W1(s) for any given system?
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Read this book Essentials of Robust control
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Is there a practical MATLAB implementation for controller synthesis?
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Yes, it is possible. In the following paper, they do it predefined grid. You can first design a controller stable for your grid points and verify your controller stability on the refined grid.
A nonlinear model predictive control framework using reference generic terminal ingredients
(LMIs in the equations 19)
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There are various works robust performance and mixed H-2/H-inf robust control. What is the difference between them?
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Mixed ℋ 2 and ℋ ∞ performance objectives. II: Optimal control
DOI: 10.1109/9.310031
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What is the elaboration of various control laws in comparison to each other. It means, in the level of comparison, when to take Adaptive control? when to adopt Robust control? when for Neuro-fuzzy control? when for Optimal control? when for model predictive control?
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Well, that is not a "unique response" answer. The controller's design strongly depends on the requirements, knowledge, and resources of the whole system. But, considering some mild conditions, in my opinion, a good way of star answering that hard question is understanding the "The Internal Model Principle" (See https://www.control.utoronto.ca/~wonham/W.M.Wonham_IMP_20180617.pdf)
In this sense, a controller is good as it can "capture" the system's dynamics. A common practice for the controller design is using a system model. The parts of the system that are not included in the model as external disturbances, unmodeled dynamics, noise, discretization effects, and other possible variations, are assumed as fulfilling some hypotheses.
Then, for this case, those hypotheses on the unknown effects are used for performing a stability analysis according to the proposed framework. An example is assuming bounded uncertainty, then looking for an ultimate bound for the system's trajectories. Or, another example, assuming the terms of the systems are all Lipschitz, then the systems and the uncertainties can be "dominated" linear control terms, hence the design reduces to solving an LMI.
Therefore, taking care of the details, the better the model, the better the controller. However, no model is perfect. There will always be external disturbances, unmodeled dynamics, and other possible variations that the model does not include. So, a controller is good as it can incorporate the dynamics of the system while attenuating the effect of the unmodeled dynamics and other sources of uncertainty,
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I am designing a robust deadbeat controller for a grid-connected inverter with a pre-filter. But after putting the inner and the prefilter controller, my overall system became a six order system. So want to learn from control experts, if that is possible. Also, what could be the effect of additional poles and zeros on the overall behaviour of the system. Your contribution will be highly appreciated.
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Thanks a lot for your kind answers @ Muhammad, Chukwudi, and Yew-Chung
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Hi,
Does anyone have experience with red fluorescent reporters (particularly mKate2) under various promoters, in yeast? We are particularly trying to express mKate2 under not a strong promoter and do not observe any color (compared to a robust control pDRF1-GW mKate2-T2A-mTurquoise2).
We are seeing good mRNA levels (ct values comparable to ACT1 mRNA using qRT-PCR) but cannot observe any protein product. We have also sequenced and verified integrity of the ORF.
Has anyone had similar problems with mKate2 or other fluorescent proteins? What could be some reasons why the mRNA can't be translated?
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Okay !! the problem here is your testing promoter is activating/expressing the mRNA, right?
you can check the quantitative RT-PCR for the control and your testing promoter plasmid (mRNA). Check the expression levels of control and your gene of interest.
in your case, I think you may get more expression level for control than your gene of interest. In that case, your promoter is not activating the mRNA that presents the plasmid.
RNA fold prediction programs ? yes you are right, but checking the expression level go for this.
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More precisely, in order to evaluate the controller performances, the IAE (integral of the absolute error) (or ISE: integral of the squared error) is generally used. Moreover, as well known in the HOSM theory, such controller is characterized by its sliding accuracy attained after the establishment of a real sliding motion (which mainly depend to the sampling time in the absence of noise and to the noise magnitude otherwise). The question is as follows: how can we interpret and discuss the tracking performance results provided by such HOSM controller using the both IAE criteria and SM accuracy in the same time?
In other hand, if we have different HOSM controllers (two SM-2 controllers for example), which provide the same IAE approximately but acheive a different order of sliding accuracies, how can we discuss this case?
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ISE penalizes the large errors, more, and would be preferred if you have constraint on the maximum error. However, ITAE is better than both, since it also accounts for the speed of convergence in time.
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Hi,
What are the books and/or papaers/reports that are recommended in order to understand fullly the mathematical stuff in the following book:
Robust and Optimal Control by Kemin Zhou et al.
i.e. how the thorems are constructed and the assumptions are made and ultimately how they are proved. It will be helpful to understand the historical devlopment as well.
Thanks & regards
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Dear Colleagues,
can one tell how Theorem 16.4 that appears in Robust Optimal Control by Kemin Zhou is constructed?
Thanks & regards
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We can derive the robust control problem by matrix inequalities to LMIs or use Riccati based iterative algorithms.
What's the advantages of the Riccati iterative methods such Kleinman algorithm compared with LMI ?
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Dear Soroush,
Concerning this question it must be said that opinions are often contradictory, to do this an idea on the subject I suggest you to see links on topic.
Iterative Solution of Algebraic Riccati Equations for Damped Systems
Accelerated LMI solvers for the maximal solution to a set of ...
Streamlining the state-dependent Riccati Equation controller algorithm
SDP-based approximation of stabilising solutions for periodic matrix ...
riccati: Topics by Science.gov
Best regards
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I have designed a robust controller for the control of grid tied PV system. The control involves controlling the active and reactive current reference currents in dq frame. Now i want to see if the controller is robust against any disturbances. I have decided to use part of reference signal as a disturbance. However i am not sure where to add this disturbance? I am using the universal bridge as inverter unit in simulink. Any help would be highly appreciated. Thank you.
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Dear Ammar,
welcome,
I came late to this question. There is some satisfactory answer. However, i would like to add some clarifying points. The grid connected inverter are controlled such that one fix the current delivered to grid.
The testing of such inverter is accomplished by applying unit step reference current either in phase or in quadrature phase and observing how the the output current will change with time. Here the main function of the controller is to follow the the set reference current. So, is interested in the settling time and the accuracy of the steady sate value.
In such inverters there is the DC/DC converter with the maximum power point control witch conditions the input voltage to the inverter to keep it almost constant. The role of the output current control of the inverted is to keep the output voltage constant.
You can also change the reference in up steps and down steps and see how far it will be tracked.
For more information please see the paper in the link:
If you find it useful please recommend for other colleagues.
Best wishes
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I want to initiate a discussion about the major differences between planning and control methods. This question is also related to the difference between feedforward and feedback, right?
Many computer scientists are developing power algorithms used for planning and navigation while on the other hand control theorists are also working on advanced robust control algorithms for achieving probably similar tasks. How can we integrate both and at which level?
I hope my question is relevant!
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In control theory, two main questions are usually considered for a system xdot=f(x,u) (x is the state, u is the control input):
- trajectory planning; the goal is to find a trajectory (xr(t),ur(t)) of the system with some desired properties (for instance xr(0)must be the initial state of the system, and xr(T) must be a desired final state to reach at tume T; additionally, the trajectory should satisfy some design constraints). This is an open-loop problem (stability, distrubance rejection, robustness, etc is not considered at this stage)
- feedback control: given a reference trajectory (xr(t),ur(t)), obtained for instance by trajectory planning, find a feedback law depending on the state (or more realistically on the measurement output y=h(x)), such that the reference trajectory is enforced despite unknown disturbances, errors in the models, etc. This is a closed-loop prblem.
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My objective is to track the time varying delay and at the same time design a robust control for the system under time varying delay and multiple delay under uncertain conditions.
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Please check reference below.. hope it will be helpful for you…
Regards…
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How can I design a robust PID controller for a second order plant having parametric uncertainties using h infinity. I tried using 'hinfsyn' function in matlab but it gives a higher order controller. Is it possible to convert it to a PID structure.
I also tried using 'systune' command in matlab to tune PID block in Simulink, there how to decide on TuningGoal.Senstivity class parameters (i.e. maximum sensitivity to disturbance as a function of frequency).
Thank You.
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Hinfsyn in Matlab will naturally give you a controller which has the order of the plant (second order) in your case plus the order of all the weighting functions you select. The plus of the method is that the synthesis procedure solves a convex optimization problem. So it is not trivial to reduce the resulting controller to an exact PID structure. Hinf is usually very powerful for MIMO systems, for which you do not care about the structure any more.
Further note, if you want to explicitly want to consider structured uncertainties, i.e. a defined Delta block, you need to consider a mu design.
For systune you can design controllers for which you preselect the structure of your controller in advance (therefore it is sometime called structured Hinf). For example a PID controller. This however results in a non-convex problem and may result in a local minima of your optimization problem.
If you try to reduce the sensitivity as you fo, you basically try be robust against inverse multiplicative input uncertainties at your plant input. Not sure if you can interpret your uncertainties in this form.
Bottom line, if you want to design a pure PID controller with with Hinf, systune would be the way to go as you can define your structure. However there is no method yet for which you can explicitly consider your modeled uncertainties.
Thus what you need to do is, analyze your parametric uncertainties and try to reflect them as so called weighting functions, for example on the plant input. Matlab offers you some tools for that. Generate a range of your uncertain parameters (e.g. ureal, for example frequency and damping in your second order model), then build a second uncertain order system (uss), and then try to generate a filter which covers the uncertainty (for example ucover, https://de.mathworks.com/help/robust/ref/ucover.html). Include the filter in the systune design and optimize the criteria you like (margins, response times, ect.)
Hope that helps!
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I have designed a robust controller for a 3rd order uncertain system (having only poles) described by 5 tr functions. Each tr function corresponding to a particular range of input. I want to simulate the implementation on a practical system. Which system should I consider?
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Lorenz system, Rossler system, Chua’s Circuit etc related to nonlinear dynamic analysis.
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Hi,
Selecting the H∞ controller weighting parameters is one the most important part of designing of such a good controller, however, there is no specific method in the most references to do that and most of the works have been done by the trial and error methods.
Do you have any suggestion in order to tune the H∞ controller?
Thanks.
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An approximate procedure is described in ...
M. Grimble, "Robust industrial control systems : optimal design approach for polynomial systems", Hoboken, NJ, Wiley, 2006
Simply tuning a controller so that it has a "healthy" phase margin (e.g. 60 deg) usually ensures that it also has a low H-inf norm, e.g. see ...
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Although I know that analytic functions are infinitely differentiable and the taylor series converges to the function but I want to know why they are so useful from the perspective of robust control theory? Can a non-analytic function perform as well as an analytic function?
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In nonlinear control, when the focus is on the performance of the system around an equilibrium point, we may want to design suboptimal controllers that match the optimal design in terms of the Taylor series expansion up to arbitrary order of precision. Matching high order terms in the optimal design is useful in its own right. But, one may wonder whether by matching more and more terms of the optimal control, does the suboptimal controller ever converge to the optimal design. That question's answer requires that the optimal design is an analytic function to begin with. Then, the suboptimal controller, if properly designed, will converge to the optimal design (at least locally around the equilibrium point) by matching higher and higher order control terms. Some relevant papers in this topic is
@article{luk69,
Author = {Lukes, D.~L.},
Journal = {SIAM Journal on Control},
Keywords = {Nonlinear control systems;Optimal control;Taylor series expansion},
Month = {Febuary},
Number = {1},
Pages = {75--100},
Title = {Optimal regulation of nonlinear dynamical systems},
Volume = {7},
Year = {1969}}
@article{panezakrekok2001b,
Author = {Pan, Zigang and Ezal, Kenan and Krener, Arthur J. and Kokotovi{\'c}, Petar V.},
Journal = {IEEE Transactions on Automatic Control},
Month = {July},
Number = {7},
Pages = {1014--1027},
Title = {Backstepping design with local optimality matching},
Volume = {46},
Year = {2001}}
The second paper above had a mistake which was corrected in an RG posting with the mark up on the copy of this paper, which is attached below.
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It is well known that every controller, when optimized in a proper way, will yield good results. Under such circumstances, how should I compare the relative performance of two different controllers that can help me ascertain the superiority of one controller over the other. How can I reduce the bias in tuning so as to genuinely claim the superiority of one over the other ?
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Hi Biswajit,
Thank you for me in to this discussion, but as Andres hinted earlier, there is no generic approach to compare controllers to decide which is better !
A realistic rephrase for the question of comparative performance will be something like:
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Hi
Consider the following closed loop generalized plant. P is the generalized plant, K is the controller to be designed and $\Delta$ matrix is the uncertainty matrix with the norm of smaller than one for all combination of the parameters.
I try to get the controller with H_inf design but the H_inf norm of the resulting closed loop from w_u to z_u is larger than 1. What does it mean?
I have tried to assume very power full actuation ( limitless). It never get smaller than 1. From theory means the controller is not robust. but why it is not possible to make it robust.
P.S: the real plant has two poles on origin.
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I think this situation reveals a crucial deficiency of H infinity design -- it does not consider the loop phase at all, and the loop phase can be as important as loop gain (or norm, including H infinity norm). I think this deficiency is also common in other existing classical control designs,
The following well known example may illustrate the importance of designing both gain and phase of loop transfer function L(jω). This example is about the optimal L(jω) of quadratic optimal control, and this optimal L(jω) is proven to satisfy Kalman Inequality and thus must have values only outside of the unit circle that is centered at -1 point. Because large gain |L(jω)| is bad, the real optimal values of this L(jω) must be near the origin, and these values must have phase angles between 0⁰ to +-90⁰!
In my publications such as "Observer design -- A survey" of 2015 and "Robust Control Design" of 2004 (2nd Ed.), and in my answers to ResearchGate questions such as LQ control, I stated the following 4 points:
1. State feedback control (including partial state feedback control, its weakest case is static output feedback control if there are enough outputs) , can assign eigenvalues AND eigenvectors (can be partial) and can therefore improve feedback system performance AND robustness FAR BETTER than any other forms of control, including the control designed by H infinity, because eigenvectors can determine the sensitivity and robust properties of their corresponding eigenvalues. This is also why modern/state space control theory was dominant over classical control theory in the 1960s and 70s.
2. The problem with full state feedback control is that its loop transfer function Lkx(s) CANNOT be realized by the separately designed realizing observer. This existing design procedure is the well known separation principle, and this critical problem of LTR was raised by John Doyle, but the LTR solutions of the 1980s were not satisfactory, for example even the asymptotic LTR is invalid for non-minimum-phase systems or invalid for most systems. This should be the reason of the returned attention to H infinity design and other classical designs, starting in the 1980's.
3. It can be simply proved that the unsatisfactory LTR solutions of the 1980's were due to the following of separation principle. As a result, I developed a new design procedure NOT following separation principle and not always design a full state feedback control (in the case that Lkx(s) cannot be exactly realized). I will design instead a generalized state feedback control (GSFC) which unifies the existing full state feedback control and static output feedback control as its two extreme (strongest and weakest) cases. The design of this GSFC is fully based on (not separated from, as in separation principle), the observer parameters and parameter C of system (A,B,C).
4. By being able to freely choose the observer order, I can design an output feedback compensator (OFC) that is valid for almost all systems (including most of the non-minimum-phase systems), and that can generate the GSFC signal. The actual OFC order, which equals the number of the estimated states/additional outputs, is chosen based on the actual system conditions and actual design requirements, unlike the fixed maximum order for full state feedback control and the fixed zero order for static output feedback control. The critical advantage of this OFC is that Lkx(s) of its GSFC is guaranteed realized exactly. Thus a satisfactory (general and exact) LTR solution is finally achieved, and the need of H infinity design of the 1980s is finally obviated.
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I am trying to develop a control strategy to optimize the control of output temperature in a heat exchanger, the measurements show a non-minimum phase response to step inputs (medium massflow).
I am trying to use the covariance R as means to reject this behaviour with the aid of a simple model (power balance), so when a big disturbance comes, the R value goes very high as "no believing" in the measurement, then feeding the resulting estimate to the PID controller.
Does this makes sense??
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Dear Leonardo,
Yes you use Kaman Filter or Extended Kaman Filter it's adapted to reject unwanted non minimum phase behavior.
Here are some Links and attached file in topics.
-Feedback Systems: An Introduction for Scientists and Engineers
-Feedback Systems - Control and Dynamical Systems - Caltech
-A finite-horizon adaptive Kalman filter for linear systems with unknown ...
Robust Bode Methods for Feedback Controller Design of Uncertain ...
Best regards
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In integrated direct/indirect adaptive robust control method, a standard projection mapping in adaptive control is used, where the outward unit normal vector is used to calculate the mapping. How to obtain the outward unit normal vector? Is there corresponding material to explain it? I can not find the right explanation.
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What I know about the definition of ''Robustness Property'' for a controller designed for a particular set of parameters of the system it can be said to be robust if it works well under high-gain feedback to reject the disturbance gained by the system and eliminate the effect the system parameter uncertainty. So, is there any relation between robustness of the controller and faster response time such as raise time maximum overshoot settling time etc..?
 Truly Yours
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Dear Mustafa,
In the 1st part of your Q&Ans part I think the meaning of Robust is clear to you. In the later part you have talked about transient response property of the controller. There is no direct relation between the  property of robustness and the transient response property.
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I have to design a controller using Convex Optimization and Sum of Squares technique, please suggest some papers on this. What are the advantages of using this techniques from the classical controllers or other robust controllers.
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I guess the Convex Optimization by Stephen Boyd is a good candidate.
here is the link.
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Robustness control for control systems with temporal and non-temporal constraints across temporal and interval Petri nets
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Assuming that, the H-infinity norm of the transfer function H(s) is less than 1 + delta, where delta is a small number.
How to prove that open loop transfer function (at the input plant), L(s), will approximate the target loop shape in this H-Infinity setup shown on the figure attached. 
Definitions;
Wp(s) = the target loop shape
'r' and 'nw' = the exogenous input (H-infinity framework)
'ew' and 'y' = the outputs ((H-infinity framework)
H(s) = closed transfer function from exogenous input to the outputs.
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The explicit proof is at Theorems 3.3 and 3.4 of my book, on pages 71-75.
The explicit proof can also be found at Subsection 3.1 of my paper "Observer Design -- A Survey".
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I have to design a robust Hinf controller for an LTI system which has a known input  besides disturbances and control inputs. (this input is not disturbance or control input)
{xdot}=[A]{x}+[B1]{m}+[B2]{w}+[B3]{u}
{z}=[C1]{x}
{y}=[C2]{x}
"{m}" is a known input vector (measurable), "{w}" is disturbance vector and "{u}" is a control input vector.
How can I design this controller in a MATLAB m file? ({m} is not supposed to be considered as a disturbance or control input) 
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I suggest to review the concept of Linear Matrix Inequalities (LMI or LMIs).
In that frame, you can design reliable robust controllers. See for instance:
Linear Matrix Inequalities in
System and Control Theory (SIAM).
(Stephen Boyd, Laurent El Ghaoui,
Eric Feron, and Venkataramanan Balakrishnan)
Best,
RZY
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I need hardware model
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We want Hardware model not software simulation!
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Hi all,
I'm trying to stabilize the following system in finite time
\dot x ^ n = \varphi + \gamma * u 
u is the control, \varphi and \gamma>0 are bounded with UNKNOWN bound. (Standard SMC Problem)
My objective is to force the state x to predefined neighborhood of zero ( |x|<\epsilon ) in finite time T.
with \epsilon and T are predefined and independant on \varphi and \gamma and the initial condition of x.
did any one try to solve this problem. Or did some one prove that it is IMPOSSIBLE to have this objective. 
Regards
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Dear Mohamed,
Please see the question asked by Hanei Wang through ResearchGate in March 8, 2014; a beneficial discussion with the participation of Itzhak Barkana.
-How to enhance the practical popularity of adaptive control ...
Here are links and attached files in subject.
- Robust adaptive control of a class of nonlinearly parameterized time ...
- Frontiers | Evolutionary Robotics: What, Why, and Where to ...
Best regards
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Hi,
I am looking to design a robust power oscillation damper for a large power system network. As you know, I will have to obtain the information like eigen values etc for which I could use a software . My question is their any software which allows to design my own robust controller and later on implement  with the test system and still obtain the crucial information like eigen values and time domain simulations?
Thank you in advance
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There are many software that can help you but unfortunately all are commercial. You have to spend much money in purchasing them. E.g. DSAT tools, PSSE, DigSILENT, ETAP ..... they have some programming interface by which you can extract eigenvalues and all other and code your algorithms in matlab or python, and interact with the system developed in these software.......
The power system research group from imperial college london is very famous for this type of work. You can google their group and papers to get some idea of how they are doing it.....
best regards,
Jagadeesh
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When picking up an object at a distance from its center of mass, a torque is applied to the gripper, increasing the amount of force required to maintain grip security. I've found a lot of research on torsional friction for contact surfaces and torque applied to joints within an arm but surprisingly little for this.
What is currently being done to compensate for this additional force that is needed? 
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Dear Steven,
Here are links and attached files in subject.
Robot control part 3: Accounting for mass and gravity | studywolf
-Robot Arm Tutorial - How to Build a Robot Tutorials - Society of Robots
-DIGIT FORCE ADJUSTMENTS DURING FINGER ADDITION ... - NCBI
www.ncbi.nlm.nih.gov › ... › PubMed Central (PMC)
-Development of a Force Sensitive Robotic Gripper - ACM Digital Library
Best regards
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Hi everyone,
I plan to modify some renewable energy converter structure (say PV and wind) and study their effect on low frequency oscillations in the grid. Once, I modify, I want to connect it to a grid or a large number of buses. My queries are:
1) I'm aware that most commercial and free software have their own built in models and can give information about eigen values. Is their some way so that I can similar information for my modified model?
2) How does our fellow authors test say a new robust controller that they built in a large IEEE bus system?  
Thank you in advance
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Hi Samundra,
If you are working with PSCAD/EMTDC, then there should be absolutely no problem ! It is a great one for incorporation of user defined models at all levels.
Just make sure that the installation of the package that you have access to must have adequate node capability that the intended user defined model requires - whatever it may be - a power electronic circuit, a machine, a control algo, or anything else ! The maximum number of nodes allowed is the only thing you need to watch for.
With best wishes.
-Sanjay
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Dear Friends, I am working on the following hammerstein model:
x(t)=1.5*u(t)-1.5*u(t)^2+0.5*u(t)^3;
y(t)=0.6*y(t-1)-0.1*y(t-2)+1.2*x(t-1)-0.1*x(t-2);
PID control law with time-variant PID parameters is employed:
u(t)=kp(t)*(y(t)-y(t-1)) + kd(t)*(y(t)-2*y(t-1)+y(t-2)) + ki(t)*e(t); But the control results for this System is not good!
the MATLAB code which utilizes is attached. 
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Dear Nazanin Zarenejad,
x(t)=1.5*u(t)-1.5*u(t)^2+0.5*u(t)^3;
y(t)=0.6*y(t-1)-0.1*y(t-2)+1.2*x(t-1)-0.1*x(t-2);
PID control law with time-variant PID parameters is employed:
u(t)=kp(t)*(y(t)-y(t-1)) + kd(t)*(y(t)-2*y(t-1)+y(t-2)) + ki(t)*e(t); But the control results for this System is not good. The applied code:
np=0.8; %Jacobian information of the controlled object ni=0.8; nd=0.2;
for t=3:N
if (0<=t) &&(t<50)
        r(t)=0.5;
    elseif (50<=t) && (t<100)
        r(t)=1;
    elseif (100<=t) && (t<150)
        r(t)=2;
    else
        r(t)=1.5;
    end
    t1=-0.271;
    t2=0.01832;
    yr(1)=r(t);
    yr(2)=r(t);
    T(1)=1+t1+t2;
    yr(t)=-t1*yr(t-1)-t2*yr(t-2)+T(1)*r(t-1);
    e(t)=yr(t)-y(t);
    kp(t)=0.486;     %PID parameters tuned by the CHR method
    ki(t)=0.227;
kd(t)=0.122;
    dy(t)=y(t)-y(t-1);
    d2y(t)=y(t)-2*y(t-1)+y(t-2);
    u(t)= ki(t)*e(t) - kp(t)*dy(t) - kd(t)*d2y(t);
    x(t)=1.5*u(t)-1.5*u(t)^2+0.5*u(t)^3;
    y(t)=0.6*y(t-1)-0.1*y(t-2)+1.2*x(t-1)-0.1*x(t-2);
    end
Here attached in subject.
Best regards
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The positive definiteness and boundedness of inertia matrix are related to the maximum and minimum singular values of inertia matrix. some of books are only considering the revolute joints for boundedness. so, clarify me why only revolute? why not prismatic? what if the combination of prismatic and revolute in a same chain? and Is this because of units matter (cm/m/mm and rad/deg)?
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It does not related with units and all, usually robot manipulators in most of the books are discussed with rotary joints and it does not restrict anything related to joints.
If you have time, please read Prof.S.K.Saha's book or Prof.Ghosal's book you will find the answer and if you are not satisfied you can write a mail to them. They will give you further answers.
All the best
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Hello everyone,
I am currently doing some research in multiple objects tracking using Image Based Visual Sservoing methods. I have already found some papers about the topic of IBVS in general and also about my main concers - keeping multiple objects in the field of view of the camera. Do You know some must-read papers? Maybe someone is also doing a research on similar topic ? I would not mind sharing ideas at all. 
I am also interested in methods of extracting the depth to the tracked object and in any promising ways of adaptation to uncertainy in this parameter. I am using a monocular vision.
Any help would be appreciated.
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Hi Manteusz
I would highly recommend the publications of Peter Corke and François Chaumette, their work is always in the forefront of visual servoing, and it also covers the basics for IBVS and PBVS. For starters, go with Visual Servo Control Part I and II.
Depth estimation from monocular images is quite challenging, it can be done in a geometry-based case, and is even more challenging in an unrestricted case. Maybe Cornell's work could give you some ideas.
I wish you success in your endeavour
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A closed loop speed control of a photo voltaic fed induction motor drive system was designed and controlled using a PID controller. The torque ripple which was around 4.5Nm was considerably reduced to 0.4Nm when the controller was replaced by a fuzzy logic controller. Is this value of torque ripple and hence the corresponding ripple current justifiably less for the controller to be replaced?
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The output cannot be generalised. The only way to know which of the controllers offer better result is through simulation. Any of the two controllers could yield better results
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Extended State Observer
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It has been proven since 1980 that if your system has more inputs than outputs (p > m), or is non-minimum-phase(most systems are if p = m and order n - m > 2), or rank(CB) < p for your system model (A,B,C), then the critical robustness property of your state feedback control (SFC) CANNOT be fully realized (unless your SFC is not designed for a good control but instead only for being fully realized). The existing approximate solution to this critical problem (called asymptotic LTR) is far from satisfactory either because it requires very high observer gain.
If your system unfortunately belongs to the above category (almost all non-trivial systems do), then to fully realize that critical property, you should use only partial state observer and partial SFC. That means you should design your SFC based on your observer parameters and parameter C, and you should abandon the state observer and the separation principle (design SFC and state observer separately) which has been followed by everyone for over half of a century. The complete design procedure is developed and is valid for all systems either satisfy p < m or has at least one stable transmission zero (or for almost all systems, hopefully including your system). I will stop here for details. You can find this new design in my publications. I would suggest "Observer Design -- A Survey" of 2015.
The key for an observer to realize the robust property is to eliminate its gain on system input. My result above can also be used to design a least square gain (instead of zero gain), This approximate solution is much more effective and satisfactory than asymptotic LTR, but approximations have no guarantee.
Finally, please do not be discouraged for two reasons. 1) My design is very simple and much much simpler than the loop transfer function based designs, and SFC (even partial SFC) is much much more effective than other forms of control; 2) A challenging design also means an opportunity for advancement -- you may achieve a good design not achieved by anyone before including MIT professors!
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I designed a robust controller based on H_infinity methods with help of matlab, I try to implemented this controller in hardware like (arduino,raspberry pi,pcduino...),is there an example?
or some thing can help to do that?
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Dear Khaled,
Check the REX control system which may be suitable for your application.
It provides a real-time core and an extensive library of functional blocks which may be used to design your control algorithms without a necessity of hand coding (just like in the Matlab-Simulink environment). There are development tools which you may try for free.
Various target hardware platforms are supported including Raspberry Pi. You can connect your system to the controlled plant via proper inputs/outputs in numerous ways (GPIOs, expansion boards or external devices supporting standard communication protocols).
Regards,
Martin
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Is it possible to use Sliding Mode controller for Single input multiple output system?
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You mean probably, underactuated systems, i.e. number of output grater than the number of input , like car and Vessel Tracking.
You can find some works of using Sliding mode controle this kind of systems.
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Please suggest any book or paper that can help me with this.
Thank you
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As far as I know, conventional sliding mode control technique requires the upper bounds of uncertainties to prove the Lyapunov stability.
However, sometimes estimating these bounds is very hard or almost impossible in real-world systems. So I am wondering if there are some SMC approaches that do not require the bounds of uncertainties.
Thank you very much.
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There are many SMC strategies using adaptive gain tuning. They do not require the bound on the uncertainty.
Please have a look at this chapter penned by Utkin and Poznyak. (http://link.springer.com/chapter/10.1007%2F978-3-642-36986-5_2)
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In the field of model order reduction, if all the poles lie at the same point for a higher order system, then to reduce the order of the system is very difficult. Can anyone tell me which method is suitable to reduce the system, especially in frequency domain methods?
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I think the suggestion of Prof.A. Zolotas will work best , if you are thinking of repeated stable real poles. May also try the Stability Equation method [See the Journal of the Franklin Institute]. 
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I am trying to compare no controller, with pid controller and fuzzy pid controller in matlab?
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What is the significance of full rank of the expression in the figure with reference to fault detection?
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let say y1 and y2 is one output of a MIMO system having input u1 and u2 where u1 acting as a direct manipulated input and u2 is acting as a indirectly acting manipulated input for y1 and vice verse. As long as the transmission zero is in the left half y1 is more effected by  u1. and if the transmission zero is in the right half, y1 is more effected by u2. This is a difficult situation to control. So if the transmission zero is in the imaginary axis the effect of u1 and u2 on y1 becomes equal. For more details see the following paper.
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I want to know about why fuzzy is used for boiler controls instead of other controllers such as model predictive controllers or robust controllers using u-synthesis technique?
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I would appreciate a reference showing that fuzzy logic is really preferred and popular in boiler control.
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What does it mean normalizing a random signal in robust control? For example, normalizing a disturbance signal and passing it through a filter to feed the plant input.
Please provide comprehensive response.
Regards,
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Why we use disturbance normalization in robust control? As you know we also use a weighted transfer function to pass the normalized disturbance signal through it, why we use this transfer function and how to determine it?
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May I know the advantages of Sliding mode control compares to others robust controllers such as nonlinear PID etc?Could anyone provide with literatures that highlight about the advantages of sliding mode controller if applied to AUV? 
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Dear Mohd Bazli Mohd Mokhar,
Matched means that the disturbance is matched with the input, in the sense that (considerinc a state space representation) they acts on the same states derivative. State space representation is a representation in term of first order odes. Lets take an example
x1 and x2 are the states, u is the input, d is the disturbance
system:
dot_x1 = x2
dot_x2 = x2 + x1 + u
system with matched disturbance:
dot_x1 = x2
dot_x2 = x2 + x1 + u + d
system with NON matched disturbance:
dot_x1 = x2 + d
dot_x2 = x2 + x1 + u
In the latter case SMC cannot reject the disturbance.
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For calculating the smoothness of the controller
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Yes, total variation of controller output can be positive or negative. It also depend on your final control element saturation limits or constraints.
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I have some dificulties to understand how to compute the parameter 'p' in the algorithm in order to determine the deflating subspace Q (algorithm 2 step 3).
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You can get the similar or apropriate answer by searching the keyword in the GOOGLE SCHOLAR page. Usually you will get the first paper similar to your keyword.
From my experience, this way will help you a lot. If you still have a problem, do not hasitate to let me know.
Kind regards, Dr ZOL BAHRI - Universiti Malaysia Perlis, MALAYSIA
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Hi,
I developed a H-infinty controller, however I would like to extend with anti-windup. In  S. Skogestad and I. Postlethwaite: MULTIVARIABLE FEEDBACK CONTROL book,there is a short description about the Hanus form, I tried to implement it using Matlab/Simulink, but the controller get unstable. Can anybody provide me a simple Matlab/Simulink example for a MIMO system with anti-windup? 
Regards,
Robert
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What's the problem with the Hanus form explained in the Skogestad book? in the loop shaping process, you need to W1 and W2 to shape the plant and then synthesise the controller based on the shaped plant. When you add the anti-windup part, you control signal instead of being u=W1Us becomes eq. (9.109) which is u = [Aw-BwDw^-1Cw 0 BwDw^-1;Cw Dw 0][Us; Ua]. Us being the input to the shaped plant and Ua the actual plant input. I have implemented that on SISO system and it did work. However, I haven't tried it on MIMO systems. I might be able to 
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I want to design a feedforward controller using LMI. Can you recommend me a good method to design this type of controller using for example Hinf approche or publication on this subject?
Regards
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Mariusz, I suggest you to start with basics. Take a look at this doc:
It contains example implementations in MATLAB. Also read this question:
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In open loop control to output transfer function of dc to dc converter, on which factor does the order of zeros depend on? As in case of order of poles  which depends on the number of passive elements present in the converter circuit.
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o/p tf ? anyways zeros result from differentiation of input. Check it in your circuit if input is differentiated.
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Sliding Mode Controller is a Robust Controller, So to reduce the chattering any Type of linear controller such as (PID) added to SMC, Is it robust?
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I search for a comprehensive document about Adaptive Robust Control (ARC) and its method. Can anyone help me to introduce or provide me a document in this subject?
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There are several methods for  solving this problem. One being efficient is to state the  contribution of  the unmodeled dynamics as an additive signal in the output (or the filetered  output) and since this is unknown/ unmeasurable to be effectively used , an upper-bounding function for the contribution of the uncertainty dynamics is  assumed known. Then,  the adaptive scheme for  parameter estimation has a relative dead  adaptation zone  so that the adaptation only takes place if the identification error modulus is sufficiently large related to the contribution of the uncertainty upper-bounding function. This avoids identification under small errors which can be due to the uncertainty contribution and which would lead to high errors in the identification since the identification acts on the nominal part of the system whose parametrization structure  is known, that is tries to identify the nominal part.  See  also some attached papers.
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I have an uncertain plant. I need to describe it using a number of transfer functions by conducting an experiment. I want to use Hudzovic method of identification and modelling.
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(1) Usually we use Hudzovic method of identification to estimate the model of a high-order system from the step response.
For example, the transfer function of a high-order system is given as
G(s)=K*exp(-Ds)/((Ts+1)^n)
where Hudzovic method of identification can be used to estimate K, T, n, and D
Indeed you can refer to numerous methods of system identification, in addition to Hudzovic method of identification.
The methods and references of system identification have been discussed in the following RG question
"What is the best reference for system identification?"
The following IEEE CST 2001 paper shows how to apply system identification approach to estimate the gain margin and phase margin of the real-world control system.
W.K. Ho, T.H. Lee, H.P. Han, and Y. Hong, "Self-Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment," IEEE Transactions on Control Systems Technology, 9(3), May 2001, pp. 535-541. Available in the following RG Link.
H. Nyquist (Sweden) --> K.J. Astrom (Sweden) --> W.K. Ho (Sweden)
     | Nyquist plot (published in 1932) 
     |  Bell Labs
    V  Bode plot (published in 1940)
H.W. Bode (Harvard) --> K.S. Narendra (Harvard, Yale) --> T.H. Lee (Yale)
(2) To design a control system with an uncertain plant, you can consider model-free control, iterative feedback tuning, fuzzy-logic, etc.
* Model-free control has been discussed in the following RG question
"Does Model Free Control (intelligent PID) have the same classical PID drawbacks, like integarl windup, sensitivity of derivative term to noisy data?"
* Iterative feedback tuning
 
Date back to 1990s, H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin proposed Iterative feedback tuning (IFT) approach to tune controller parameters for those control model (or control plant) whose parameters are difficult to be identified relatively accurately using system identification approach.
[HGGL98] H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, "Iterative feedback tuning: theory and applications," IEEE Control Systems Magazine, vol.18, no.4, Aug 1998, pp .26-41,
By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with the PID controller to solve controller tuning issues caused by plant uncertainty of nonlinear system. H. Hjalmarsson was elected to the Class of 2013 IEEE fellow last year due to his fundamental contribution to iterative feedback tuning.
WK Ho, Y Hong, A Hansson, H Hjalmarsson, and JW Deng, "Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157. Available in the following RG Link.
* Fuzzy logic
(3) Recent discussions on control system design approaches can be found in the following RG link.
"What are trends in control theory and its applications in physical systems (from a research point of view)?"
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Terminal SMC and its variants are finite time controller based on sliding mode control. Is there any other robust and finite time controlller available?
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Dear Mr Kumar
in SMC you should to use sign function or sat,..........
terminal SMC is used to reduce the chattering . This type of SMC is used to reduce the chattering as well as improve the stability and robust. I think this type of controller should to compare with boundary layer SMC or the other type of chatter free SMC.
Regards
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I am working with a humanoid robotic arm. The joints have dc servo motor with position and velocity sensor. But the sensor data is delayed. I have come across several methods including delayed input, transmission delay in telerobotic system etc. But it will be very helpful if somebody could guide me to which type of method I should follow. 
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Dear Farzin Piltan,
It has been a while since I worked with non-linear manipulators and backstepping, but in my experience it is very difficult to deal with time-delay in feedback in practice, and makes it very difficult to analyze stability for non-linear systems (I can't remember ever having seen any standard/general approach for analyzing the effect of time-delay in non-linear systems).
With regards to backstepping, I guess the more practical option is to rely on the observer you usually have to design for the backstepping control law, and the feedback of these states together with the feed-forward of the reference through the chosen dynamical model. In my experience then, the more accurate the model is, the better results you get. The simple approach is to reduce/change the gains by trial and error (simulation) in order to find an implementation that is stable (although stability can still not be guaranteed), but of course this increases the bound for the error. I guess this is the trade-off that has to be made. The robustness of backstepping (the varieties that I have seen) really do not extend to the effects of time-delay (and also, notably, does not handle sensor/actuator saturations, which can be a problem since backstepping often generates huge control signals, unless the growth rate of the control law terms is limited...)
I guess a different approach of using an Hinfinity control law (which includes an Hinfinity obeserver/generalized Kalman filter) and feed-forward linearization could be used. This might be a simpler framework to work with since it is possible to include the effects of time-delay in the linear model. Time-delay here also tends to restrict the control law gains, and depending on accuracy of the linearization, the linear model uncertainty can be large, and the two problems combined might make the performance poor, but I guess it is hard to say in general.
Changing the sensors (reducing the actual time-delay), if that is possible, does sounds like the very best option to me... Optical encoders should be really fast if used correctly. For rapid-prototyping and hardware-in-the-loop simulations, I would in general suggest using a regular PC running the MATLAB xPC real-time operating system with a National Instruments DAQ card installed (http://sine.ni.com/ds/app/doc/p/id/ds-15/), since it is usually a fast and relatively inexpensive solution that works without much modification, and since many of the DAQ cards include fast encoder inputs.
That is what I think, anyway :)
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I know it is very general question but it makes me confused, because I've read many papers most of those use PD sliding surface and some use PID surface, but there are some papers that use different types of sliding surface and may they used auxilary state. I want to know how can I formulate the state equation for auxilary state.
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Dear Ali
It's a general question, but you must to know that if you want to have a best result, sign function help you to have a good result  but it has some challenges. you can design higher order SMC or terminal SMC also. if you would like to have any information you also can follow my work.
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In many papers, we use homogeneous controller of negative degree, so that we proof the asymptotic stability to deduce the finite time stability.
Let us take, the pure double integrator system
\dot x = y; \dot y = u,
with u = -l*sign(y + |x|^0.5sign(x))
according to Levant and Emelyanov, for $l > 0.5$, our system is finite time stable. I agree.
Now, let us take $0<l<0.5$ (l=0.25 for ex.), we can prove that the closed loop system is asymptotically stable, but it seems that the convergence is only asymptotic, not finite time.
Am I right?
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Negative homogeneity degree+asymptotic stability always imply finite-time stability.
In the considered case you probably get "twisting-like" convergence.
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The switching model of dc/dc converter is averaged and linearized to obtain the small signal model (SSM). SSM is then used to design controllers such as PI, state-feedback-controller etc, which can achieve control objective after tuning. Now, when disturbance is introduced this controller seems to amplify the disturbances, such that open-loop plant performs better than closed-loop. I want to achieve disturbance cancellation by disturbance-feed-forward. So, my question is how to go about this as the available techniques for disturbance observers seems not to work because in order to achieve such, the system has to be minimum-phase, however, the PWM converter in question is non-minimum-phase. Any idea here?
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So, I saw these articles http://link.springer.com/article/10.1007/s12555-010-0508-x#page-1, http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=6617950&abstractAccess=no&userType=inst, giving a shot on how to deal with nonminimum phase systems using disturbance observer. I think they are good starting point. I think the major challenge comes from the fact that internal dynamics of different systems makes it harder to realise the conventional disturbance observer. So, the disturbance observer has to reflect on the system at hand.
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How does iPID deal with input and output constrains (especially when there are strict upper and lower output bounds)? Does that affect its performance? And to what extent?
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Even Intelligent PID control is not model free control, since you need the an accurate model of the system to design the controller, however intelligent methods such as GA could be used for fine tuning. A good example of model free controllers is Fuzzy Logic Control, where as exact model of the system is not required for design stage.
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I want to implement a High GA in Observer for a non-mimnimum phase TORA system. Do I have to apply only extended HGO or will a simple HGO suffice?
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Yes check the khalil Boker paper and Nazrulla paper.
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Can anyone help me with the algorithm used in fitfrd (used to be fitsys in the previous MATLAB versions)? I know that the command is used to fit the frequency response data with a state space representation model. I want to know the algorithm that is used in these two commands. The MATLAB help document didn't help. By the way, this command (fitfrd) is in Robust Control Toolbox and the (fitsys) was available in mu-synthesis and analysis Toolbox.
Thanks.
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(1) Both fitfrd and fitsys can be regarded as mu-synthesis approach proposed for robust control system design.
fitfrd means Fit D-scaling frequency response data with state-space model.
fitfrd delivers a state space representation of a fitted transfer function to the given frequency response of the controller.
The book [OS75] provides the detailed introduction of fitfrd.
[OS75] A.V. Oppenheim and R.W. Schaffer, Digital Signal Processing, Prentice Hall, New Jersey, 1975, p. 513.
fitsys attempts to fit given scalar frequency response data in both magnitude and phase (with a SISO system). This algorithm is based heavily on the algorithm invfreqs. The book [LS88] provides more details.
[LS88] J . N. LITTLE and L. SHUREL, The signal processing toolbox, Mathworks 1988.
(2) The papers [Zames66] and [DGKF89] are two landmark papers in robust control system design.
G. Zames, "On the Input-Output Stability of Time-Varying Nonlinear Feedback Systems--Part I: Conditions Derived Using Concepts of Loop Gain, Conicity, and Positivity; Part II: Conditions Involving Circles in the Frequency Plane and Sector Nonlinearities, " IEEE Transactions on Automatic Control, AC–11, 1966.
The paper [Zames66] was selected by IEEE Control Society as "Control Theory developed in the twentieth century: 25 Seminal Papers (1932-1981)" in 2000.
[DGKF89] JC Doyle, K Glover, PP Khargonekar, and BA Francis, "State-space solutions to standard H2 and H∞ control problems," IEEE Transactions on Automatic Control, 34(8), 1989, pp. 831-847.
The paper [DGKF89] received IEEE W.R.G. Baker Outstanding Paper Award (The most outstanding paper reporting original work in one of the IEEE publications). It is the first time the award has been given to a paper in the control area.
(3) The following paper applied the robust control approach proposed by [Zames66] in Internet bandwidth congestion control.
Y. Hong and O.W.W. Yang, "Robust Explicit Congestion Controller Design For High Bandwidth-Delay Product Network: A H∞ Approach," Proceedings of IEEE International Conference on Communications (IEEE ICC), Cape Town, South Africa, May 2010.
Available in the following RG link.
(4) Recent discussions on control system design approaches can be found in the following RG link.
"What are trends in control theory and its applications in physical systems (from a research point of view)?"
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I did some research in this area and I want to be aware of other researcher's favorites.
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I have the following problem. Consider a system \dot x1 = \mu f1(x1,x2,x3), \dot x2=\mu f2(x1,x2,x3), \dot x3 = f3(x1,x2,x3), where 1 \le \mu \le M and f_i's are polynomial. If I find a Lyapunov function in the vertex \mu = 1 and a Lyapunov function in the vertex \mu = M, can I conclude that the system is asymptotically stable for all 1 \le \mu \le M?
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It depends. The reason is this: The fundamental assumption is that your system \dot{X} = f(X) where X represents the variables x1, x2 and x3, has a fixed point X*. Your Lyapunov function is a continuously differentiable real-valued function V(X) such that: (i) V(X)>0 for all X \neq X* and V(X*)=0, and (ii) \dot{V} < 0 for all X \neq X*; only when these two conditions are met, the fixed point X* is globally asymptotically stable. Hence the "depends" in the opening sentence; your parameter \mu could change the stability of your system. Therefore, provided that there are no bifurcations of f(X) for 1 \le \mu \le M, then the system is globally asymptotically stable at a fixed point X*. A final comment: you can claim that your system is asymptotically stable around a given fixed point; this precision is important because you could have multiple fixed points, and not all are necessarily asymptotically stable even if you find a Lyapunov function that works in one of them.
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The requirement of the controller to force the system output to follow the reference output model as closely as possible is the existence of G and H.
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(1) The idea of "robust tracking and model following" was originally proposed by Hopp and Schmitendorf in the following paper.
T.H. Hopp and W.E. Schmitendorf, “Design of a linear controller for robust tracking and model following,” ASME Journal of Dynamic Systems, Measurement, and Control, 112(4), December 1990, pp. 552-558.
The goal of an ideal linear control system design is that the system output y(t) can track the reference input y_m to make tracking error decrease to zero. However, Hopp and Schmitendorf claimed that "The tracking error does not asymptotically decrease to zero because the systems are uncertain, instead the tracking error is bounded."
"the tracking error is bounded" can also be regarded as "the system uncertainty is bounded" which is the requirement of robust control theory.
You can read G. Zames's two seminal papers among "Control Theory developed in the twentieth century: 25 Seminal Papers (1932-1981) Selected by IEEE Control Society in 2000" as shown in the following link.
Therefore, Hopp and Schmitendorf proposed the matrix [A B;C 0][G;H]=[G.Am;Cm] to design a linear controller for a linear system with time-varying uncertainty.
To simplify their linear controller design, Hopp and Schmitendorf "force the system output to follow the reference output model" so that "the tracking error is bounded".
That is, "The requirement of the controller to force the system output to follow the reference output model as closely as possible is the existence of G and H such that [A B;C 0][G;H]=[G.Am;Cm]."
"If a solution cannot be found to satisfy the matrix [A B;C 0][G;H]=[G.Am;Cm], then a different reference model has to be chosen."
This can be regarded as the constraint or the limitation of the linear controller design for "robust tracking and model following".
(2) Quote Saleh Mobayen's two questions:
(a) "How we define the matrix?"
The definition of the matrix [A B;C 0][G;H]=[G.Am;Cm] can be found in the above original paper by Hopp and Schmitendorf, or other follow-up papers as shown in the following link.
(b) "How can we reach this model?"
We can obtain the model using the state space representation. That is, x(t)^\dot=Ax(t)+Bu(t), y(t)=Cx(t).
You can read R.E. Kalman's three seminal papers among "Control Theory developed in the twentieth century: 25 Seminal Papers (1932-1981) Selected by IEEE Control Society in 2000" as shown in the following link.
(c) In addition, the following 3 papers illustrate how to obtain the model for a control system using the state space representation.
J.B. He, Q.G. Wang, and T.H. Lee, "PI/PID controller tuning via LQR approach," Chemical Engineering Science, 55(13), July 2000, pp. 2429-2439.
Y. Hong and O.W.W. Yang, "Self-Tuning Optimal PI Rate Controller for End-to-End Congestion With LQR Approach," Proceedings of 20th International Teletraffic Congress (ITC-20), Ottawa, Canada, June 2007, pp.829-840. Available in the following RG link.
Y. Hong, “The Controller Design For Linear System: A State Space Approach,” Technical Report, National University of Singapore, November 1999. Available from the following RG link.
The following paper applied the maximum modulus theorem proposed by G. Zames's seminal paper to design the controller where "the system uncertainty is bounded" or "the tracking error is bounded".
Y. Hong and O.W.W. Yang, "Robust Explicit Congestion Controller Design For High Bandwidth-Delay Product Network: A H∞ Approach," Proceedings of IEEE International Conference on Communications (IEEE ICC), Cape Town, South Africa, May 2010. Available in the following RG link.
 
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I designed a robust controller based on H_infinity methods in MATLAB. How to implement the designed robust controller in Real Time using Micro-controller or DSP? What are the difficulties for real time implementation? Are there any standard procedures?
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a well known way is to use MATLAB’s xPC Target two PC-type desktop computers in a host-target configuration, and a NI BNC-2110 data acquisition card. as in "Robust H ∞ Controller for High Precision Positioning System, Design, Analysis, and Implementation" .Intelligent Control and Automation 01/2012; 333030:262-273. DOI:10.4236/ica.2012.33030
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I am using PXR5 TCY1-1V070 Fuji PID controller for heating my specimen for a controlled heating with ramp function. I am interested in heating the specimen (aluminium block) at a specific rate as fast as possible (ramp time 1 min). I want to heat the specimen from 25 Deg C to 43 Deg in one min. I did Autotunning (AT) at the fixed set point 43 Deg. Got some P, I and D values. I want to use ramp function for heating where I have set parameters as follows SV1 (target1)---25, TM1r (Ramp time)---0.01, TM1S (soak segment time)--0.03, SV2 (target2)---43, TM2r (Ramp time)---0.01, TM2S (soak segment time)--0.08. But significant overshooting is observed each time i.e. specimen gets heated to 50 Deg C although second target point is 43 Deg C. Along with this the target temperature is not achieved in given ramp time (1 min) it takes more time. There is lag between SV and PV where as SV follows ramp time properly but ideally PV should follow SV for successful completion of ramp soak function. I contacted engineer he asked me to double P value but its not working on the contrary the heating is taking more time than that is set .
I am using band type heater and J type thermocouple.
Kindly suggest the solution to avoid over heating. What parameter do I need to adjust so that the ramp soak function will work properly?
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Two suggestions:
1) apply the D term in an inner loop to avoid a zero appearing on the closed-loop transfer function - this zero usually causes overshoot (also known as derivative kick)
2) because the reference function is known a priori, apply some feed-forward and use the feed-back to account for the disturbances and plant uncertainty.
If you are constrained by your choice of hardware then contact the supplier to find out if controller structure can be re-programmed.
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Suppose, you are able to get only the position information with noise. If the velocity is less vulnerable to noise, we can estimate the volocity and to noise filtering and convert to position if necessary.
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Obtaining velocity from position requires differentiation which amplifies noise at high frequencies.
Obtaining position from velocity requires integration which amplifies noise at low frequencies (i.e. the bias will be amplified). From another point of view, integration is semi-stable, so any bias will accumulate and cause the position estimate to drift.
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How to calculate control effort for a second order system with PID controller?
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P(s) is plant TF, G(s) is controller then, control effort can be obtained as G(S)/(1+P(s)G(s)).