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ABSTRACT: This paper illustrates the practical application of non-iterative correlation-based tuning with guaranteed stability. In this method, a sufficient condition for closed-loop stability is defined as the H<sub>∞</sub>-norm of a particular error function. This norm is then estimated using data from one closed-loop experiment. The method is applied to a pick-and-place robot. It is shown that the proposed constraints for stability are effective without being overly conservative. Furthermore, it is shown how the method can be used to systematically design low-order controllers.
Control Applications (CCA), 2010 IEEE International Conference on; 10/2010
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ABSTRACT: All H <sub>∞</sub> controllers of a SISO LTI system are parameterized thanks to the relation between Bounded Real Lemma and Positive Real Lemma. This new parameterization shares the same features with Youla parameterization, namely on the convexity of H <sub>∞</sub> norm constraints for the closed-loop transfer functions. However, it can deal with low-order controllers and can be extended easily for the systems with polytopic uncertainty. The effectiveness of the proposed method is shown via an academic example.
IEEE Transactions on Automatic Control 10/2010; · 2.11 Impact Factor
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ABSTRACT: In this paper, an iterative-learning-control (ILC) algorithm is proposed for a certain class of linear parameter-varying (LPV) systems whose dynamics change between iterations. Consistency of the algorithm in the presence of stochastic disturbances is shown. The proposed algorithm is tested in simulation and the obtained tracking performance is compared with that obtained using a standard linear time-invariant ILC algorithm. Better results are obtained using the proposed method. The method is also applied to a linear, permanent-magnet synchronous motor system, which is shown to be an LPV system for a specific class of movements. Greatly improved tracking is achieved.
IEEE/ASME Transactions on Mechatronics 07/2010; · 2.87 Impact Factor
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ABSTRACT: In this paper an Iterative Learning Control (ILC) algorithm is proposed for a certain class of Linear Parameter Varying (LPV) systems whose dynamics change between iterations. Consistency of the algorithm in the presence of stochastic disturbances is shown. The proposed algorithm is tested in simulation and the obtained tracking performance is compared with that obtained using a standard Linear Time Invariant ILC algorithm. Better results are obtained using the proposed method.
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
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ABSTRACT: A new approach for robust fixed-order H<sub>∞</sub> controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by a finite set of complex values in the frequency domain are considered. It is shown that the H<sub>∞</sub> robust performance condition can be approximated by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The proposed method is compared with the standard H<sub>∞</sub> control problem. It is shown by an example that for an unstable uncertain model, a PID controller can be designed with the proposed approach which gives better H<sub>∞</sub> performance than a 7th order unstable controller obtained by the standard H<sub>∞</sub> solution.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: Methods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed parameterisation of the precompensator, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: In a recent work, a frequency method based on linear programming was proposed to design fixed-order linearly parameterized controllers for stable linear multi-model SISO systems. The method is based on the shaping of the open-loop transfer functions in the Nyquist diagram under a set of linear constraints guaranteeing a lower bound on the crossover frequency and a linear stability margin. In this paper, this method is extended to guarantee quadratic stability. For this purpose, new linear constraints based on the phase difference of the characteristic polynomials of the closed-loop systems are added in the Nyquist diagram. A simulation example illustrates the effectiveness of the proposed approach.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: This paper presents a data-driven controller tuning algorithm that includes a sufficient condition for closed-loop stability. This stability condition is defined by a set of convex constraints on the Fourier transform of specific auto-and cross-correlation functions. The constraints are included in a correlation-based controller-tuning method that solves a model-reference problem. This entirely data-driven method requires a single experiment and can also be applied to nonminimum-phase and unstable systems. The resulting controller is guaranteed to stabilize the plant as the data length tends to infinity. The performance with finite data length is illustrated through a simulation example.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: High-performance output tracking can be achieved by precompensator or feedforward controllers based on the inverse of either the closed-loop system or the plant model, respectively. However, it has been shown that these inverse controllers can adversely affect the tracking performance in the presence of model uncertainty. In this paper, a model-free approach based on only one set of acquired data from a simple closed-loop experiment is used to tune the controller parameters. The approach is based on the decorrelation of the tracking error and the desired output and is asymptotically not sensitive to noise and disturbances. From a system identification point of view, the stable inverse of the closed-loop system is identified by an extended instrumental variable algorithm in the framework of errors-in-variables identification methods. By a frequency-domain analysis of the criterion, it is shown that the weighted two-norm of the difference between the controller and the inverse of the closed-loop transfer function can be minimized. The method is successfully applied to a high-precision position control system.
IEEE Transactions on Control Systems Technology 10/2008; · 1.77 Impact Factor
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ABSTRACT: Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as a linear matrix inequality (LMI) using the Kalman–Yakubovich–Popov (KYP) lemma. This parameterization is a convex inner approximation of the whole nonconvex set of stabilizing controllers, and depends on the choice of a central polynomial. It is shown that, with an appropriate choice of the central polynomial, the set of all stabilizing fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis can be outbounded with some LMIs. These LMIs can be used for robust pole placement of polytopic systems.
IEEE Transactions on Automatic Control 03/2008; · 2.11 Impact Factor
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ABSTRACT: The estimation of a system's infinity norm using one set of measured input and output data is investigated. It is known that, if the data set is noise free, this problem can be solved using convex optimization. In the presence of noise, convergence of this estimate to the true infinity norm of the system is no longer guaranteed. In this paper, a convex noise set is defined in the time domain using decorrelation between the noise and the system input. For infinite data length, we prove that the estimate of the infinity norm converges to its true value. A simulation example shows the behavior for finite data length. In addition, the method is used to test closed- loop stability in the context of data-driven controller tuning. A sufficient condition for stability in terms of an infinity norm is introduced. The effectiveness of the proposed stability test is illustrated via a simulation example.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
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ABSTRACT: A quadratic programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants represented by spectral models. The method is based on the shaping of the open-loop or closed-loop frequency functions in the Nyquist diagram. The quadratic error between a desired open loop transfer function and the actual open loop frequency function is minimized in the frequency domain subject to linear constraints guaranteeing stability and robustness margins by quadratic programming. Moreover, it is shown that the H infinity mixed sensitivity robust performance problem can be approximated by linear constraints and be integrated in the control design method. The method can directly consider multi- model as well as frequency-domain uncertainties. An application to a difficult benchmark problem illustrates the effectiveness of the proposed approach.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
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ABSTRACT: An overview of the recent works on proportional integral derivative (PID) controller tuning methods based on specifications on the infinity-norm of the sensitivity functions is presented. The presented approach is very flexible relative to the controller structure and the a priori knowledge about the process. It can be applied to plants described by parametric models, frequency domain non-parametric models as well as in a model-free framework. For the latter, procedures for measuring the design parameters values are described. The problem is then solved by minimising iteratively a frequency criterion, defined as the weighted sum of squared errors between the actual values and desired values of the design parameters. If the plant is described by a parametric model, model uncertainty can be handled to guarantee stability and performance robustness of the designed closed-loop system. Simulation examples are provided to compare the results obtained with the proposed approach to those resulting from well-accepted PID controller tuning methods. An application of the proposed method to a double-axis permanent-magnet synchronous motor illustrates the effectiveness of the approach to control of systems with large uncertainties.
IET Control Theory and Applications 02/2007; · 0.99 Impact Factor
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ABSTRACT: Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, firstly by a statistical analysis and then by their application to a linear motor. Expressions for the expected value and variance of the error are developed for each algorithm. The different algorithms are then applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectrums are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate
IEEE Industrial Electronics, IECON 2006 - 32nd Annual Conference on; 12/2006
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ABSTRACT: A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A lower bound on the crossover frequency and a new linear stability margin which guarantees lower bounds for the classical robustness margins are defined. Two optimization problems are proposed and solved by linear programming. In the first one the robustness margin is maximized for a given lower bound on the crossover frequency, whereas in the second one the integrated error is minimized with constraints on the new stability margin. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach
American Control Conference, 2006; 07/2006
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ABSTRACT: Friction modeling of a high-precision positioning system using linear permanent magnet synchronous motors is investigated. The friction force is measured precisely by some specific experiments to eliminate the parasitic ripple force. The experimental data show that the relation between the lubrication force and the velocity is not linear as it is assumed in the conventional friction models used in automatic control. A new model for the lubrication force based on tribological observations is proposed and introduced to the LuGre friction model. The new model can characterize the lubrication force saturation which is encountered in the acquired data. The parameters of the new friction model are identified and compared with the standard ones
American Control Conference, 2006; 07/2006
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ABSTRACT: This paper presents a PID controller design method for stable minimum-phase systems. The approach is similar to the one proposed in the so-called modified Ziegler-Nichols method, where only one point on the frequency response of the plant is measured and then moved to the desired position on the unit circle. This technique provides the specified phase margin and crossover frequency to the closed-loop system. However, the ratio between integral and derivative time is not fixed prior to the design in the proposed approach. This ratio is chosen is order to obtain the desired loop slope at the crossover frequency. Constraints on the infinity-norm of sensitivity functions are used to shape the loop transfer function and to determine the corresponding loop slope value. The proposed method, which is based on Bode's integral relationships for the slope adjustment, does not require any parametric model of the plant and can be applied with only modest effort
American Control Conference, 2006; 07/2006
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ABSTRACT: High performance output tracking can be achieved by precompensator or feedforward controllers based on the inverse of the closed-loop system or the plant model. However, it has been shown that these inverse controllers can affect adversely the tracking performance in the presence of model uncertainty. In this paper, a model-free approach based on only one set of acquired data from a simple closed-loop experiment is used to tune the controller parameters. The approach is based on the decorrelation of the tracking error and the desired output and is not asymptotically sensitive to noise and disturbances. By a frequency-domain analysis of the criterion, it is shown that the weighted two-norm of the difference between the controller and the inverse of the plant model (or the closed-loop transfer function) can be minimized. The method is successfully applied to a high precision position control system.
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
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ABSTRACT: The recently-proposed method for iterative correlation-based controller tuning is considered in this paper for the tuning of multivariable Linear Time-Invariant (LTI) controllers. The parameters of the controller are updated directly using the data acquired in closed-loop operation. This approach allows one to tune some elements of the controller transfer function matrix to satisfy the desired closed-loop performance, while the other elements are tuned to mutually decouple the closed-loop outputs. The controller parameters are calculated by minimization of the cross-correlation function involving instrumental variables. A very simple choice of the instruments is proposed. The approach is applied to a simulation model of a gas turbine engine, and excellent results are obtained in terms of decoupling and performance.
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
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ABSTRACT: This paper gives an overview on the theoretical results of recently developed algorithms for iterative controller tuning based on the correlation approach. The basic idea is to decorrelate the output error between the achieved and designed closed-loop systems by iteratively tuning the controller parameters. Two different approaches are investigated. In the first one, a correlation equation involving a vector of instrumental variables is solved using the stochastic approximation method. It is shown that, with an appropriate choice of instrumental variables and a finite number of data at each iteration, the algorithm converges to the solution of the correlation equation. The convergence conditions are derived and the accuracy of the estimates are studied. The second approach is based on the minimization of a correlation criterion. The frequency analysis of the criterion shows that the two norm of the error between the desired and achieved closed-loop transfer functions is minimized independent of the noise characteristics. This analysis leads to the definition of a generalized correlation criterion which allows the mixed sensitivity problem to be handled in two norm. Copyright © 2004 John Wiley & Sons, Ltd.
International Journal of Adaptive Control and Signal Processing 09/2004; 18(8):645 - 664. · 0.91 Impact Factor
