Computation of stabilizing PI-PD controllers

The PI-PD controller structure provides an excellent four-parameter controller for control of integrating, unstable and resonant processes to set point changes while the conventional PID controller has limitations in controlling such systems. In this paper, a graphical method for the computation of all stabilizing PI-PD controllers is given. The proposed method is based on plotting the stability boundary locus, which is a locus dependent on the parameters of the controller and frequency, in the parameter plane. The stability boundary loci are first obtained in the (K _d , K _f ) and (K _p , K _i ) planes and then it is shown that all the stabilizing values of the parameters of a PI-PD controller can be found. Computation of stabilizing PI-PD controllers which achieve user specified gain and phase margins is also studied. The method is used to design robust PI-PD controllers for control systems with parametric uncertainties. A design procedure for interval control systems is proposed. Examples are given to show the benefit of the method presented. Recommended by Editorial Board member Jietae Lee under the direction of Editor Young Il Lee. Nusret Tan was born in Malatya, Turkey, in 1971. He received his B.Sc. degree in Electrical and Electronics Engineering from Hacettepe University, Ankara, Turkey, in 1994. He received the Ph.D. degree in Control Engineering from University of Sussex, Brighton, U.K., in 2000. He is currently working as an Associate Professor in the Department of Electrical and Electronics Engineering at Inonu University, Malatya, Turkey. His primary research interest lies in the area of systems and control.     

Formulas for a class of controllable and observable sublanguages larger than the supremal controllable and normal sublanguage

In this paper, we give some new methods for synthesis of controllers of discrete event dynamical systems (DEDS) with partial event informations. Given a regular target language L, we construct some effective computable algorithms for computing the controllable and observable sublanguages of L. We show that any one of these controllable and observable sublanguages obtained by our algorithms is larger than the supremal controllable and normal sublanguage of L.     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.     

A new look at the robust control of discrete-time Markov jump linear systems

In this paper, we make a foray in the role played by a set of four operators on the study of robust H₂ and mixed H₂/H_∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H₂ performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H₂ controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H₂/H_∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.     

Parameterization of Sampled‐Data H∞ Output Feedback Controllers for General Nonlinear Systems

In this paper, we consider the H^∞ control problem for general nonlinear systems under sampled measurements. Sufficient conditions for the existence of H^∞ output feedback controllers are derived. The major contribution of this paper is to characterize a family of H^∞ output feedback controllers for nonaffine nonlinear systems under sampled measurements.     

Adaptive neuro-genetic control of chaos applied to the attitude control problem

Conventional adaptive control techniques have, for the most part, been based on methods for linear or weakly non-linear systems. More recently, neural network and genetic algorithm controllers have started to be applied to complex, non-linear dynamic systems. The control of chaotic dynamic systems poses a series of especially challenging problems. In this paper, an adaptive control architecture using neural networks and genetic algorithms is applied to a complex, highly nonlinear, chaotic dynamic system: the adaptive attitude control problem (for a satellite), in the presence of large, external forces (which left to themselves led the system into a chaotic motion). In contrast to the OGY method, which uses small control adjustments to stabilize a chaotic system in an otherwise unstable but natural periodic orbit of the system, the neuro-genetic controller may use large control adjustments and proves capable of effectively attaining any specified system state, with no a prioriknowledge of the dynamics, even in the presence of significant noise.This work was partly supported by SERC grant 90800355.     

Robust satisfactory fault-tolerant control of uncertain linear discrete-time systems: an LMI approach

Fault-tolerant control is an important issue in practical systems. Based on satisfactory control and estimation theory, a passive fault-tolerant control strategy is proposed for a class of uncertain linear discrete-time systems in this article. Manipulating linear matrix inequality (LMI) technique, robust fault-tolerant state-feedback controllers are designed which take the possible actuator faults and sensor faults into consideration, respectively. The closed-loop systems are guaranteed by the designed controllers to meet the required constraints on regional pole index φ(q, r), steady-state variance matrix X index and control-cost function V ²(u) index simultaneously. Then, whether possible faults occur or not, the closed-loop systems would maintain the three desirable performance indices accordingly. Meanwhile, the consistency of the performance indices mentioned earlier is also discussed for fault-tolerant control.     

Non‐fragile H ∞ control for switched stochastic delay systems with application to water quality process

In this paper, the problem of non‐fragile observer‐based H _∞ control for discrete‐time switched delay systems is investigated. Both data missing and time delays are taken into account in the links from sensors to observers and from controllers to actuators. Because data missing satisfies the Bernoulli distribution, such problem is transformed into an H _∞ control problem for stochastic switched delay systems. Average dwell time approach is used to obtain sufficient conditions on the solvability of such problems. A numerical example and a real example for water quality control are provided to illustrate the effectiveness and potential applications of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance and robustness preservation in MIMO systems when applying SPR Substitutions†

We are concerned in this article with controlled linear time-invariant multi input multi output systems in continuous-time. We study here the preservation under strict positive real substitutions (of zero relative degree) of coprime factorisations as well as stabilising properties in parametrised controllers. We also tackle here both the preservation of well-posedness (of the tracking feedback control scheme) and the preservation of H _∞-optimality properties in some classes of closed-loop systems affected by multiplicative unstructured uncertainty, including the so-called suboptimal H _∞-control problem by stable controllers (i.e. preservation of both strong stabilisation and H _∞-boundedness).     

Reliable nonlinear control system design using duplicated control elements

Reliable L₂ gain bounding (i.e., H_∞) controllers for nonlinear systems are designed by using redundant control elements. One sensor and one actuator are duplicated, and the resulting closed-loop system is reliable with respect to both the single contingency case and the primary contingency case. The design procedures for reliable controllers are developed by using the Hamilton–Jacobi inequalities from nonlinear H_∞ control theory. Linear reliable controller design methods are also obtained by restricting the proposed nonlinear methods to the linear case, and the linear methods are found to be less conservative than existing methods for linear reliable controller design. Examples are given to illustrate the design procedures for both linear and nonlinear reliable controllers and the advantages of the proposed linear method over existing ones. © 1997 by John Wiley & Sons, Ltd.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Lower bound analysis of H ∞ performance achievable via decentralized LTI controllers

This paper is concerned with the decentralized H _∞ controller synthesis problem for discrete‐time LTI systems. Despite of intensive research efforts over the last several decades, this problem is believed to be nonconvex and still outstanding in general. Therefore, most of existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficulty, in this paper, we propose convex optimization procedures for computing lower bounds of the H _∞ performance that is achievable via decentralized LTI controllers of any order. In particular, we will show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting. We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Singular L2‐gain control for switched nonlinear control systems under arbitrary switching

This article concerns with the synthesis of L₂ ‐gain state feedback controllers, without the standard regular assumption, for multi‐input switched nonlinear control‐affine systems under arbitrary switching. A common control storage function approach is developed for deriving sufficient conditions for the existence of uniform L₂ ‐gain controllers. Moreover, an explicit formula for constructing L₂ ‐gain controllers is presented. A numerical example is given for illustration.     

On the 2-induced norm of a sampled-data system

Formulas are given for the norms of SG and GH: G is a linear continuous-time system, S an ideal sampler, and H a zero-order hold; the signal spaces are ₂(−∞, ∞) (continuous-time) and l₂(Z) (discrete-time). These formulas are then applied to problems of uniformly optimal control of sampled-data systems.     

On the design of a reduced-order H ∞ controller for nonlinear sampled-data systems

In this paper, the problem of designing reduced-order H ^∞ controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential game, sufficient conditions are derived for the existence of such reduced-order H ^∞ controllers. These conditions are expressed in terms of the solutions of two Hamilton–Jacobi inequalities, comprising a standard Hamilton–Jacobi inequality and a differential Hamilton–Jacobi inequality with jumps. These Hamilton–Jacobi inequalities are exactly those used in the construction of full-order H ^∞ controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers. An illustrative example is also included.     

Switched Second‐Order Sliding Mode Control with Partial Information: Theory and Application

This paper proposes a novel switched second order sliding mode (S‐SOSM) control strategy in a partial information setting, i.e., when only the sliding variable is accessible for measurements. Such a control approach allows one to deal with systems characterised by different levels of uncertainties associated with different regions of the state space and to accommodate different control objectives in the different regions by switching among appropriate SOSM controllers. The proposed approach is shown to ensure global finite‐time convergence to the origin of the closed‐loop system trajectory. The braking control of two‐wheeled vehicles is considered as a case‐study to test the controller performance.     

Control design for chained-form systems with bounded inputs

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not continuous at the origin and although they provide exponential rates of convergence, they may use significant amount of control effort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing bounded controllers (with exponential convergence rates) for nonholonomic systems in chained form.     

An Alternative approach to H∞ control for fuzzy systems

In this paper the problem of H_∞ dynamic feedback control for fuzzy dynamic systems has been studied. First the problem of H_∞ dynamic feedback controller designs for complex nonlinear systems, which can be represented by Takagi‐Sugeno (T‐S) fuzzy systems, is presented. Second, based on a Lyapunov function, four new dynamic feedback H_∞ fuzzy controllers are developed by adequately considering the interactions among all fuzzy sub‐systems and these dynamic feedback H_∞ controllers can be obtained by solving a set of suitable linear matrix inequalities. Finally, two examples are given to demonstrate the effectiveness of the proposed design methods. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Piecewise Envelope Approach to H ∞ Control of Nonlinear Systems

This paper provides a computable approach for the H _∞ control synthesis of nonlinear systems using the piecewise envelope method. Firstly, the computation method of piecewise envelope is presented such that the required piecewise linear differential inclusions (PWLDIs) can be obtained by solving a linear optimization problem. Then, we propose the H _∞ control design method for PWLDIs using piecewise Lyapunov function theory, all the synthesis conditions are formulated as the feasibility of linear matrix inequalities, hence computationally tractable. Because of the inclusion relationship, the H _∞ controllers designed for PWLDIs are also effective for original nonlinear systems. The validity of the proposed approach is tested by application to control a wheeled mobile robot.