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Assessment of controller output saturation in dynamic systems: a case of performance, efficiency and system stress trade-off
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An accurate host power model is necessary for effective power management in data centers which is crucial for reducing energy consumption and cost. One should evaluate the power models for different workloads and host configurations. We have analyzed several existing power models by varying the workload type (CPU, memory, and disk-intensive) and host configurations. By analyzing the system performance and nature of the power consumption of the hosts, we have identified some performance counter parameters that determine the system power consumption. We have proposed three power models based on multi-variable Linear Regression, Support Vector Regression (SVR), and Artificial Neural Network (ANN). Experimental results show that compared to the existing models, our proposed power models, especially those based on SVR and ANN, more accurately predict the power consumption of the hosts. We have also conducted simulation experiments to show the importance of the power model in the energy-efficient resource management of the hosts in the data center. Results show that the use of our SVR-based and ANN-based power models in a resource management approach can effectively decrease the energy consumption of the data center. Moreover, we have proposed an energy-efficient virtual machine (VM) placement and consolidation algorithm that further reduces energy consumption. At first, we formulated a model using integer linear programming. Then, we designed a heuristic based on Vogel’s Approximation Method. Extensive simulation on the CloudSim platform with benchmark workload data and the Google Cloud trace logs shows that our approach outperforms the state-of-the-art algorithms under comparison in terms of energy efficiency and quality of service (QoS). The results also highlight the importance of a suitable VM placement and consolidation approach and an accurate power model in reducing energy consumption.
This article presents the study of the stability of single-input and multiple-input systems with point or distributed state delay and input delay and input saturation. By a linear transformation applied to the initial system with delay, a system is obtained without delay, but which is equivalent from the point of view of stability. Next, using sufficient conditions for the global asymptotic stability of linear systems with bounded control, new sufficient conditions are obtained for global asymptotic stability of the initial system with state delay and input delay and input saturation. In addition, the article presents the results on the instability and estimation of the stability region of the delay and input saturation system. The numerical simulations confirming the results obtained on stability were performed in the MATLAB/Simulink environment. A method is also presented for solving a transcendental matrix equation that results from the process of equating the stability of the systems with and without delay, a method which is based on the computational intelligence, namely, the Particle Swarm Optimization (PSO) method.
Climate change is profoundly affecting nearly all aspects of life on earth, including human societies, economies, and health. Various human activities are responsible for significant greenhouse gas (GHG) emissions, including data centers and other sources of large‐scale computation. Although many important scientific milestones are achieved thanks to the development of high‐performance computing, the resultant environmental impact is underappreciated. In this work, a methodological framework to estimate the carbon footprint of any computational task in a standardized and reliable way is presented and metrics to contextualize GHG emissions are defined. A freely available online tool, Green Algorithms (www.green‐algorithms.org) is developed, which enables a user to estimate and report the carbon footprint of their computation. The tool easily integrates with computational processes as it requires minimal information and does not interfere with existing code, while also accounting for a broad range of hardware configurations. Finally, the GHG emissions of algorithms used for particle physics simulations, weather forecasts, and natural language processing are quantified. Taken together, this study develops a simple generalizable framework and freely available tool to quantify the carbon footprint of nearly any computation. Combined with recommendations to minimize unnecessary CO2 emissions, the authors hope to raise awareness and facilitate greener computation.
This article presents a control strategy to improve the energy efficiency of a quadrotor for field inspections. A power consumption analytical model for a quadrotor is constructed, which indicates that the power consumption of a quadrotor is correlated with the roll and pitch angles. Based on that, a cascaded bounded control framework is developed to regulate the roll and pitch angles within the predefined energy-efficient ranges, while a successful inspection trajectory tracking can be achieved simultaneously. Experimental studies are carried out to prove the effectiveness of the proposed method through a mock-up scenario of wind farm inspection. Compared to the conventional cascaded control framework, the proposed energy saving control strategy is capable of saving 5% energy for the same inspection assignment under wind disturbance.
The Chua's circuit has been considered as one of the most important paradigms for nonlinear science studies. Its simulations is usually undertaken by means of numerical methods under the rules of IEEE 754-2008 floating-point arithmetic standard. Although, it is well known the propagation error issue, less attention has been given to its consequences on the simulation of Chua's circuit. In this paper we presented a simulation technique for the Chua's circuit, it exhibits qualitative differences in traditional approaches such as RK3, RK4 and RK5. By means of the positive largest Lyapunov exponent we show that for the same initial condition and same set of parameters, we produce a periodical and a chaotic solution.
A lower bound error for free-run simulation of the polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is introduced. The ultimate goal of the polynomial NARMAX is to predict an arbitrary number of steps ahead. Free-run simulation is also used to validate the model. Although free-run simulation of the polynomial NARMAX is essential, little attention has been given to the error propagation to round off in digital computers. Our procedure is based on the comparison of two pseudo-orbits produced from two mathematical equivalent models, but different from the point of view of floating point representation. We apply successfully our technique for three identified models of the systems: sine map, Chua's circuit and Duffing–Ueda oscillator. This technique may be used to reject a simulation, if a required precision is greater than the lower bound error, increasing the numerical reliability in free-run simulation of the polynomial NARMAX.
It is very important for energy conservation and environmental protection to realize energy-saving control of central heating system by prediction method. In this paper, the system model of central heating is built according to the general principle of secondary heating network, and an energy-saving control scheme based on the combination of dual networks and the regulation of secondary heating network is developed. In order to achieve better energy-saving control, the echo state network method is used to predict the heating water temperature in the heat exchange station controller. In the configuration process of echo state network, the water supply circuit temperature of the secondary heating network is taken as the output, and the 8 parameters of the primary heating network and the secondary heating network are taken as the input. After the stable echo state network is obtained through iterative training, the prediction is completed by using iterative multi-step method. Through the experimental results of three groups of sample data, it can be seen that the echo state network and prediction method constructed in this paper are superior to other methods, and are suitable for energy-saving prediction of central heating system.
This paper presents a novel design process of decoupled PI current controller for permanent magnet synchronous generator (PMSG)-based wind turbines feeding a grid-tied inverter through back-to-back converter. Specifically, the design methodology consists of combining disturbance observer-based control (DOBC) with feedback linearization (FBL) technique to ensure nominal transient performance recovery under model uncertainty. By simplifying the DOBC under the feedback linearizing control, it is shown that the composite controller reduces to a decoupled PI current controller plus an additional term that has the main role of recovering the nominal transient performance of the feedback linearization, especially under step changes in the reference. Additionally, an anti-windup compensator arises naturally into the controller when considering the control input saturation to design the DOBC. This permits to remove the effect of the saturation blocks required to limit the control input. The proposed control scheme is implemented and validated through experimentation conducted on 22-pole, 5 kW PMSG. The results revealed that the proposed technique can successfully achieve nominal performance recovery under model uncertainty as well as improved transient performances under control saturation.
5th ed. Introduction to control systems -- Mathematical modeling of control systems -- Mathematical modeling of mechanical systems and electrical systems -- Mathematical modeling of fluid systems and thermal systems -- Transient and steady-state response analyses -- Control systems analysis and design by the root-locus method -- Control systems analysis and design by the frequency-response method -- PID controllers and modified PID controllers -- Control systems analysis in state space -- Control systems design in state space -- Appendix A : Laplace transform tables -- Appendix B : Partial-fraction expansion -- Appendix C : Vector-matrix algebra.
In this paper, an iterative learning control (ILC) approach is proposed for a class of nonlinear multi-input-multi-output (MIMO) systems with unknown nonparametric uncertainties and input saturations. The nonlinear system is assumed to be under state alignment condition. The proposed scheme can address the nonparametric uncertainties which satisfy the local Lipschitz condition. Also, the proposed control law can deal with the input saturations which widely exist in the practical fields. By designing the composite energy function (CEF), we prove the convergence of the tracking error along the iteration axis. From the proof, we can see that the proposed control approach can warrant a L 2 [0, T] convergence of the tracking error. Finally, we give an numerical simulation to demonstrate the effectiveness of the ILC approach.
Inverted pendulum control is a well-known and challenging problem, which is generally associated to attitude control of a rocket during takeoff. This paper describes the method for stabilizing and trajectory tracking of Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). The main focus of this paper is to design a stabilizing controller which can accommodate the disturbance present in the system in the form of an external force. In order to understand the importance of an optimal LQR controller, a Proportional-Integral-Derivative (PID) controller is also implemented in this paper. Simulation results prove that the proposed LQR controller can guarantee the inverted pendulum a faster and smoother stabilizing with less oscillation and better robustness than a PID controller.
Power electronics plays an important role in the control and conversion of modern electric power systems. In particular, to integrate various renewable energies using DC transmissions and to provide more flexible power control in AC systems, significant efforts have been made in the modulation and control of power electronics devices. Pulse width modulation (PWM) is a well developed technology in the conversion between AC and DC power sources, especially for the purpose of harmonics reduction and energy optimization. As a fundamental decoupled control method, vector control with PI controllers has been widely used in power systems. However, significant power loss occurs during the operation of these devices, and the loss is often dissipated in the form of heat, leading to significant maintenance effort. Though much work has been done to improve the power electronics design, little has focused so far on the investigation of the controller design to reduce the controller energy consumption (leading to power loss in power electronics) while maintaining acceptable system performance. This paper aims to bridge the gap and investigates their correlations. It is shown a more thoughtful controller design can achieve better balance between energy consumption in power electronics control and system performance, which potentially leads to significant energy saving for integration of renewable power sources.
Power electronics plays an important role in the control and conversion of modern electric power systems. In particular, to integrate various renewable energies using DC transmissions and to provide more flexible power control in AC systems, significant efforts have been made in the modulation and control of power electronics devices. Pulse width modulation (PWM) is a well developed technology in the conversion between AC and DC power sources, especially for the purpose of harmonics reduction and energy optimization. As a fundamental decoupled control method, vector control with PI controllers has been widely used in power systems. However, significant power loss occurs during the operation of these devices, and the loss is often dissipated in the form of heat, leading to significant maintenance effort. Though much work has been done to improve the power electronics design, little has focused so far on the investigation of the controller design to reduce the controller energy consumption (leading to power loss in power electronics) while maintaining acceptable system performance. This paper aims to bridge the gap and investigates their correlations. It is shown a more thoughtful controller design can achieve better balance between energy consumption in power electronics control and system performance, which potentially leads to significant energy saving for integration of renewable power sources.
This paper presents the design of predictive control
with state constraints for the swing-up and stabilizing control of
a cart with an inverted pendulum system where the state
constraints are proposed on angle and velocity of pendulum,
position and velocity of cart, Since the system has strong
nonlinearity and inherent instability, a step of linearization is
necessary to extract linear state space model. Then the discretetime
predictive controller is applied to the linearized system ,
where the general design objective of this one is to compute a
trajectory of a future manipulated variable u in order to walk
the cart along a setpoint trajectory while keeping the pendulum
to the equilibrium position. Maintaining the pendulum in the
balanced position is achieved by including state constrained in
control objective where the basic idea is to translate the state
constraints problems to linear inequalities then parameterize
them using the same parameter vector ΔU as the only one used in
the design of predictive control, in order to relate to the original
model predictive control problem, then the optimal solution is
found by solving a quadratic optimization problem. Simulation
results show clearly the effect of taking the state constraints in
the control design in keeping the pendulum at the balanced
position while moving the cart in predefined trajectory
Tbe Genesis of Chua's Circuit Following a non-technical personal reminiscence of the author's conception of Chua's circuit, this paper presents the systematic sequence of technical steps which the author used to design his chaotic circuit. The design procedure. though straightforward in na-ture. could not have been concocted without a work-ing knowledge of several crucial properties of nonlin-ear circuits and their physical realizations. Die Entstehung der Chua-Schaltung Anhand eines personlichen. nichttechnischenRiickblicks auf die Grundgedanken des Autors zur Chua-Schaltung stellt die Arbeit die systematische Folge der technischen Schritte dar, die ihn zum Entwurf dieser chaotischen Schaltung ffihrten.Der Entwurfsvorgang ist an sich recht einfach. erforderte aber dennoch die Erfahrung und Kenntnis verschiedener Kerneigenschaften nichtlinearer Schaltungen und ihrer physikalischen Realisierungen.
A representation of intervals is proposed that, instead of both endpoints, uses the lower endpoint and the width of the interval. This proposed representation is more efficient since both endpoints have many corresponding bits that are equal. Consequently, the width of the interval can be represented with a smaller number of bits than an endpoint, resulting in a better utilization of the number of bits available. Considering the case in which the total number of bits is the same as for the traditional representation (say, two double-precision floating-point numbers) we determine the number of bits of the lower endpoint and of the width so that the rounding error is minimized. The use of this combination of bits would result in a variable representation, which is difficult to implement. Alternatively, it is possible to use a fixed partition that gives good results for a variety of applications.
The proposed representation is evaluated for several computations. Using a total number of 128 bits to represent the interval we conclude that it produces intervals that are substantially narrower than those obtained with the traditional representation.
Alternative implementations of the calculation of the width are proposed. The interval widths produced are shown to be very similar, so that the choice of the alternative can be made by considerations such as area and delay.
To tackle the twin challenges of sustainable energy supply and climate change, numerous efforts have been made to decarbonize the whole energy systems. Control Engineering, which concerns the automated operation of a machine or system to achieve desired target(s) and to avoid unstable or unintended disruptive behavior, has played a key role in modern industry and across the whole energy system. Advanced control technologies, such as optimal control, provide a framework to simultaneously regulate the system performance and limit control energy. However, little has been done so far to exploit the full potential of controller design in reducing the energy consumption while maintaining desirable system performance. This paper for the first time investigates the correlation between control energy consumption and system performance, and shows that this correlation is nonlinear and the controller design should be a delicate synthesis procedure to achieve better trade-off between system performance and energy saving.
This paper presents the modelling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using Proportional-Integral-Derivative (PID) controller and Linear Quadratic Regulator (LQR). LQR, an optimal control technique, and PID control method, both of which are generally used for control of the linear dynamical systems have been used in this paper to control the nonlinear dynamical system. The nonlinear system states are fed to LQR which is designed using linear state-space model. Inverted pendulum, a highly nonlinear unstable system is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches at a desired position and the inverted pendulum stabilizes in upright position. The MATLAB-SIMULINK models have been developed for simulation of control schemes. The simulation results justify the comparative advantages of LQR control methods.
Due to rounding errors results obtained by numerical simulations of nonlinear systems may be unreliable. It is however possible to carry out the computations in such a way that the results obtained are rigorous. In this paper several tools based on interval analysis are presented. Methods for computing trajectories, techniques for finding accurate enclosures of attractors, interval operators for proving the existence of fixed points and periodic orbits, and methods for proving the existence of nontrivial symbolic dynamics, are described. Computational techniques are illustrated by performing validated numerical analysis of the Hénon map and the Chua's circuit.
From the Publisher:
This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theoryand shows how to solve all computational problems with MATLAB. It avoids highly mathematical arguments, and features an abundance of examples and worked problems throughout the book. Chapter topics include the Laplace transform; mathematical modeling of mechanical systems, electrical systems, fluid systems, and thermal systems; transient and steady-state-response analyses, root-locus analysis and control systems design by the root-locus method; frequency-response analysis and control systems design by the frequency-response; two-degrees-of-freedom control; state space analysis of control systems and design of control systems in state space.
In this work, an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation. The analysis of convergence in the iteration domain is based on composite energy function, which consists of both input and state information along the time and iteration axes. Through rigorous analysis, the learning convergence in the iteration domain can be guaranteed under the input saturation, provided the desired trajectory is realizable within the saturation bound.
Numerical methods for the solution of ordinary differential equations are one of the main tools used in the theoretical investigation of nonlinear continuous dynamical systems. These replace the continuous dynamical system under study by a discrete dynamical system that is then usually simulated on a digital computer. It is well known that such discrete dynamical systems may be chaotic even when the underlying continuous dynamical system is not chaotic. We here show that some numerical methods may produce discrete dynamical systems that are not chaotic, even when the underlying continuous dynamical system is thought to be chaotic. We find in this case that the transition to chaos from false stability mimics the transition to chaos that has been previously observed as parameters were changed in the Rössler system.
Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.
Input saturation is inevitable in many engineering applications. Most existing iterative learning control (ILC) algorithms that can deal with input saturation require that the reference signal is realizable within the saturation bound. For engineering systems without precise models, it is hard to verify this requirement. In this note, a “reference governor” (RG) is introduced and is incorporated with a range of existing ILC algorithms (primary ILC algorithms). The role of the RG is to re-design the reference signal so that the modified reference signal is realizable. Two types of the RG are proposed: one modifies the amplitude of the reference signal and the other modifies the frequency. Our main results provide design guidelines for two RGs. Moreover, a design trade-off between the convergence speed and tracking performance is also discussed. A simple simulation result verifies the effectiveness of the proposed methods.
In this tutorial, an approach to the analysis and design of linear
control systems based on numerical convex optimization over closed-loop
maps is presented. Convexity makes numerical solution effective: it is
possible to determine whether or not there is a controller that achieves
a given set of specifications. Thus, the limit of achievable performance
can be computed. To provide a context for the material presented, a
brief overview of control engineering is given. A broad outline of
various approaches to control design for linear and time-invariant
systems is presented, including their advantages and disadvantages, for
purposes of comparison with the approach presented. It is shown that
many performance specifications have natural and useful geometric
interpretations, and the notion of a closed-loop convex design
specification is defined. The performance requirement that the
closed-loop system be stable is discussed. It is shown that many
performance specifications can be expressed as convex constraints on
closed-loop performance specifications, and how some of these can be
expressed as convex constraints on closed-loop transfer matrices is
examined
The first step in investigating the dynamics of a continuous-time system described by an ordinary differential equation is to integrate to obtain trajectories. In this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge–Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.
State constrained predictive control of cart with inverted pendulum
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A novel design of pi current controller for pmsg-based wind turbine considering transient performance specifications and control saturation
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