Robust Control System Design Research Articles

Robust and simple adaptive control system design

AbstractRecently, the simple adaptive control (SAC) method has attracted considerable interest because of the simple structure of its adaptive controller. The method can only be applied to plants with so‐called almost strictly positive real (ASPR) characteristics. Unfortunately, most real plants do not satisfy this condition. Furthermore, real plants contain disturbances such as uncertain elements. This paper deals with such problems and proves that the implementation of a parallel feedforward compensator makes it possible to apply the SAC method to non‐ASPR SISO plants with plant uncertainties. Furthermore, a robust SAC algorithm in the presence of a class of external disturbances is also considered. The effectiveness of the parallel feedforward compensator and robust adaptive controller designed in this way is examined through several numerical simulations.

Robust design of discrete-time systems via optimization

Abstract An optimization approach for the design of robust discrete-time control systems is presented. Using pole clustering, the design specifications for the system time response are recast in the form of inequality constraints governing the free design parameters. Quantitative robustness and disturbance rejection measures are discussed using Lyapunov matrix equations. A performance index combining the robustness and disturbance rejection measures is minimized subject to the parameter inequality constraints to obtain the desired design. A numerical example is given to illustrate the usefulness of the design approach.

Robust flight-path control system design with multiple-delay model approach

Robust control system design with a multiple-delay model approach is applied to a flight-path and velocity control problem. The approach is based on concepts of multiple models, linear quadratic regulator, and proportional output feedback. Multiple-delay models are used to represent uncertain dynamics in the high-frequency range. The performance index is defined with a quadratic function presenting the design goal in a natural manner, and the control law is obtained by minimizing the performance index. The control law obtained by the multiple-delay model approach is robust against unstructured uncertainty and is a natural extension of the linear quadratic regulator to increase the robustness without performing complicated adjustments of the quadratic performance-index weighting matrices. A flight-path and velocity control problem for a lightweight transport is studied to examine feasibility of the approach. Crossover frequency and phase margin, frequency-response matrix singular values, control performance change due to the parameters' variation, and command input time responses including nonlinear dynamics effects are studied to demonstrate the robustness of the control laws. Numerical results show the feasibility and usefulness of the approach.

Robust control and H∞-optimization—Tutorial paper

The paper presents a tutorial exposition of H ∞-optimal regulation theory, emphasizing the relevance of the mixed sensitivity problem for robust control system design.

A study on nonlinear robust adaptive control system design of industrial robotic manipulators : Sung Hyun Han, Man Hyoung Lee, pp 345–350

A study on nonlinear robust adaptive control system design of industrial robotic manipulators : Sung Hyun Han, Man Hyoung Lee, pp 345–350

Robust control system design with state constraints

Abstract A new design methodology that yields robust controllers for globally or locally linearized model is introduced. The linear models are used together with eigen-structure assignment to select suitable dynamics for the system. The selected eigen-structure is assigned to a linear regulator with prescribed relative stability. The satisfaction of state inequality constraints is checked using a published method due to Kiendl. After the designs are completed, their robustness is assessed using a new measure of robustness. The process is repeated until satisfactory robustness, relative stability, etc. are achieved. The design methodology is illustrated using a 2-DOF robotic manipulator example. The example shows that the final design selected must be a compromise between robustness, relative stability, gain magnitude and other considerations.

A review of quantitative feedback theory as a robust control system design technique

Performance robustness has been an important issue in control and it has been increasingly recognised as an area of significance in many design applications. This issue has particular importance among the engineering community because it offers a solution to control system design problems for plant and processes that cannot be described by a single linear time-invariant model. The aim of this paper is to describe one of the methods available for robust control system design called Quantitative Feedback Theory (QFT) and discuss its application to engineering problems. QFT is a powerful design technique based on multi degree-of-freedom use of feedback. The basic building block of a multi-degree-of-freedom system is a two-degree-of-freedom system in which two controllers are present, one inside the feedback loop, used to reduce closed-loop uncertainty, and the other prior to the loop, used to shape the input in order to achieve the required output. To show the power of the method, the application to an aero engine described by a non-linear model, linearised at five operating conditions, is discussed. A comparison of the QFT method is also made with the H-infinity method. It is shown that the H-infinity formulation of the QFT problem can produce a more conservative solution than the QFT method.

Book Review: Robust Control System Design Using H-infinity and Related Methods

Book Review: Robust Control System Design Using H-infinity and Related Methods

A methodology for sequential design of robust decentralized control systems

A general analysis theory is presented which can incorporate robust stability or robust performance defined in H ∞ or μ framework for sequential design purposes. As a result, a methodology for sequential design of robust decentralized controllers is proposed. To do so, new formulations of linear fractional transformation of complementary sensitivity function and sensitivity function are given. They are used to derive robustness constraints on individual decentralized controllers. When these robustness constraints are satisfied, the closed-loop system is a guaranteed to possess pre-specified robustness properties if and only if the whole system is nominally stable as well.

A Study on Nonunear Robust Adaptive Control System Design of Industrial Robotic Manipulator

This paper presents new and simple robust adaptive control system for the implementation of real time control of the multi-joint robot manipulator. Based-on the linearized dynamic equation, the adaptive control scheme used a least square identification(LSAC) is designed to perform the online parameter estimation of the feedback controller gains. Next, the nonlinear robust adaptive control system(NRAC) is designed to perform the robust and real-time control of desired trajectory tracking under the existence of the unknown payload variation and inertia parameter uncertainties. In LSAC scheme a recursive least-square identification scheme is used to estimate the feedback gain matrix directly, not to estimate the inertia parameters of manipulator. The feedback gains of the controller are updated and adjointed in each sampling time to achieve the desired control performance. In NRAC the proposed adaptive control algorithm is developed within the framework of adaptive model following control theory using the Lyapunov Direct Method. The performance of the proposed adaptive control algorithm is compared with a similar adaptive control scheme. To demonstrate the effectiveness of proposed control system, simulation is performanced under the existence of error of inertia parameter and unknown payload.

Robust control systems design using H-infinity optimization theory

In this paper, we show step-by-step procedures for applying the H°° theory to robust control systems design. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H°° control theory. We will review the physical meanings of the H°° norm, explain how it relates to robustness issues, and show how to formulate H°° optimization problems, including the construction of a state-space realization of the generalized plant. An efficient algorithm is used to compute the optimal H°° norm. The controller formulas of Glover and Doyle are slightly modified and are used to construct an optimal controller without any numerical difficulty.

Mimo Process Identification for Controller Design: Test Signals, Nominal Model and Error Bounds

Advanced MIMO (multi-input multi-output) control design techniques need accurate process models. Process identification is an effective way to do industrial process modelling. In this work, some problems in MIMO process identification are studied, where the purpose of identification is control system design. First a recent result on prediction error method identification will be introduced which is the theoretical basis of the work. Then a procedure of MIMO process identification is proposed which consists basically high order model estimation and model reduction. The method of identification is numerically simple and reliable. A special feature of the method is that it can not only estimate a nominal parametric model of the process, but also supply an upper bound of the model uncertainty (modelling errors) in the frequency domain. Input design can be solved easily in this approach. The identified nominal model and error bound can be readily used for robust control system analysis and design. An industrial application is presented to validate our method.

Optimal transfers between coplanar elliptical orbits

Nesline, F. W., and Zarchan, P., Why Modern Controllers Can Go Unstable in Practice, Journal of Guidance, and Dynamics, Vol. 7, No. 4, 1984, pp. 495-500. Miyazawa, Y., and Dowell, E. H., Robust Control System Design with Multiple Model Approach and Its Application to Active Flutter Control, AIAA Guidance, Navigation and Control Conference, AIAA Paper 89-3578, Boston, MA, Aug. 1989. Miyazawa, Y., and Dowell, E. H., An Approach to Modeling and Estimation for Uncertain System, AIAA Guidance, Navigation and Control Conference, AIAA Paper 87-2241-CP, Monterey, CA, Aug. 1987; see also Journal of Guidance, and Dynamics, Vol. 12, No. 5, 1989, pp. 672-680. Data Set Handbook of the Dornier Do228-200 Aircraft, BM20-32/ 88, Dornier Friedrichshafen, Germany, 1988. Bryson, A. E., Jr., and Ho, Y. C., Applied Optimal Blaisdell, Waltham, MA, 1969.

Robust flight control system design with multiple model approach

References 1 Lukes, D. L., Differential Equations: Classical to Controlled, Academic, New York, 1982, Chap. 8. Kretz, M., Aubrun, J. N., and Larch, M., Wind Tunnel Tests of the Dorand DH 2011 Jet Flap Rotor, Vol. 1, NASA-CR-114693, June 1973. Molusis, J. A., Hammond, C. E., and Cline, J. H., Unified Approach to the Optimal Design of Adaptive and Gain Scheduled Controllers to Achieve Minimum Helicopter Rotor Vibration, 37th Annual Forum of the American Helicopter Society, New Orleans, LA, May 1981. Johnson, W., Self Tuning Regulators for Multicyclic Control of Helicopter Vibration, NASA TP 1996, March 1982. Bryson, A. E., and Ho, Y. C., Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere, New York, 1975, Chap. 12. Wittenmark, B., Stochastic Adaptive Control Methods: A Survey, International Journal of Control, Vol. 21, No. 5, 1975, pp. 705-730. Haviland, J. K., and Knospe, C., Wide-Band, Time-Domain Adaptive Control for Helicopter Vibrations, Second Technical Workshop on Dynamics and Aeroelastic Stability Modeling of Rotorcraft Systems, Boca Raton, FL, Nov. 1987.

Stability of fuzzy control systems by using nonlinear system theory

In this paper we consider fuzzy control system as nonlinear control systems. We present an unifying framework of methodologies and summarize three different methods. The first one is based on the geometrical interpretation of the system dynamic behaviour in the phase portrait. The second uses stability and robustness indices defined from the qualitative theory of dynamic systems. The third method adopts the input-output stability approach by using the conicity criterion. These methods provide the basis for the development of new methodologies for the design of stable and robust fuzzy control systems.

Nearly decoupled robust MIMO control systems design

The paper deals with the robust design of an MIMO feedback control system. It is divided into two parts. The first part presents a necessary and sufficient condition for the robustness of a unit feedback system. The uncertainty model considered in this analysis is nontrivial, and the present approach is applicable to nearly decoupled systems as well as nondecoupled systems. The second part of the paper presents an effective technique for the design of a robust, nearly decoupled MIMO system using the result of Part I. The design technique to be presented in Part II can be applied to a nonminimum phase plant.

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and re...

Gain margins and phase margins for multivariable control systems with adjustable parameters

Abstract This paper presents a method for finding the boundaries of gain margins and phase margins of multivariable control systems with adjustable parameters. The considered systems are first decomposed into the augmented open-loop transfer functions modified by adding an analytical gain-phase margin tester, then the characteristic equations are formulated, and finally the stability equations are used to find the boundaries of constant gain margins and phase margins. The main advantage of the proposed method is to obtain complete information about the effects of adjustable parameters on gain margins and phase margins; thus it is a useful tool for analysis and design of robust control systems,

CAD of Discrete Multivariable Control Systems Using Singular Characteristic Patterns and Vectors

This paper introduces the concept of singular characteristic patterns of discrete multivariable control systems based on discrete convolution algebra. The implementation of these concepts in a new software language CBSL for simulation and computer-aided design of robust control systems is described and illustrated by the design of a robust control system for an unstable chemical reactor

The robust design of active noise control systems based on relative stability measures

This paper presents a design method for active noise control (ANC) systems operating in a three-dimensional nondispersive propagation medium based on an analysis of the relative stability of the inherent feedback loop. For practical systems the use of absolute stability is not useful; a system having an extremely long oscillatory response is unlikely to be accepted and would be liable to instability under small parameter variations. In this respect, a measure of the relative stability can provide a more acceptable design criterion. This procedure results in a robust design able to operate under changing operating conditions, with guaranteed system stability under stationary and slowly varying conditions. The frequency domain stability conditions are interpreted as spatial conditions on the geometry of the ANC system. Practical limitations in the design of the controller owing to the geometric configuration of the system are also discussed.