Sarah K. Spurgeon

Sliding mode control : theory and applications

In the formation of any control problem there will be discrepancies between the actual plant and the mathematical model for controller design. Sliding mode control theory seeks to produce controllers to over some such mismatches. This text provides the reader with a grounding in sliding mode control and is appropriate for the graduate with a basic knowledge of classical control theory and some knowledge of state-space methods. From this basis, more advanced theoretical results are developed. Two industrial case studies, which present the results of sliding mode controller implementations, are used to illustrate the successful practical application theory.

Sliding mode observers for fault detection and isolation

This paper considers the application of a particular sliding mode observer to the problem of fault detection and isolation. The novelty lies in the application of the equivalent output injection concept to explicitly reconstruct fault signals. Previous work in the area of fault detection using sliding mode observers has used disruption of the sliding motion to detect faults. A design procedure is described and nonlinear simulation results are presented to demonstrate the approach.

On the development of discontinuous observers

Abstract A framework is proposed for the development and analysis of robust observers for uncertain dynamical systems. A variable structure systems approach is used. Emphasis is placed upon the numerical tractability of the associated synthesis procedure. A selected numerical example is used to illustrate the proposed algorithm.

Sliding mode observers: a survey

Sliding mode observers have unique properties, in that the ability to generate a sliding motion on the error between the measured plant output and the output of the observer ensures that a sliding mode observer produces a set of state estimates that are precisely commensurate with the actual output of the plant. It is also the case that analysis of the average value of the applied observer injection signal, the so-called equivalent injection signal, contains useful information about the mismatch between the model used to define the observer and the actual plant. These unique properties, coupled with the fact that the discontinuous injection signals which were perceived as problematic for many control applications have no disadvantages for software-based observer frameworks, have generated a ground swell of interest in sliding mode observer methods in recent years. This article presents an overview of both linear and non-linear sliding mode observer paradigms. The use of the equivalent injection signal in problems relating to fault detection and condition monitoring is demonstrated. A number of application specific results are also described. The literature in the area is presented and qualified in the context of continuing developments in the broad areas of the theory and application of sliding mode observers.

SLIDING MODE STABILIZATION OF UNCERTAIN SYSTEMS USING ONLY OUTPUT INFORMATION

A practical procedure is presented for synthesizing output feedback controllers for uncertain systems based on sliding mode concepts. The class of systems to which the results apply is identified and includes the requirement that the nominal linear system is minimum phase. The procedure proposed for the design of the sliding surface uses established output feedback eigenvalue assignment results. It will be shown that all the assumptions imposed on the system pertain to the design of the sliding surface. The proposed controller, which guarantees attainment of a sliding mode despite the presence of uncertainty requires no additional assumptions.

Hyperplane design techniques for discrete-time variable structure control systems

The design of variable structure control schemes for uncertain discrete-time systems is considered. Previous work in this area which parallels the discrete-time sliding mode philosophy with that for the continuous-time case is reviewed. Theoretical results are presented which indicate that such a parallel approach is not necessarily desirable. A novel design methodology for discrete-time variable structure control systems is then formulated. A numerical example is given to illustrate the results described.

Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty

In this paper, a robust stabilization problem for a class of uncertain systems is studied using sliding mode techniques. Matched and mismatched uncertainties are both considered. By employing the sliding surface proposed by Edwards and Spurgeon in [Int J Control 1995; 62(5): 1129–1144], the stability of the sliding mode is shown first. Then, an asymptotic observer is established to estimate the system state variable based on a constrained Lyapunov equation, and a variable structure controller is proposed to stabilize the system by exploiting the estimated state and system output. The two major limitations in [IEEE Trans Autom Control 1996; 41(11): 1691–1693] are eliminated. Finally, a simulation study based on a simplified model of the HIRM aircraft system is used to illustrate the effectiveness of the results.

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.

A nonlinear control strategy for robust sliding mode performance in the presence of unmatched uncertainty

It is well known that sliding mode control schemes provide robustness to the class of uncertainty acting within channels implicit in the control inputs: the so-called matched uncertainty. However, the unmatched uncertainty will affect the ideal dynamics prescribed by the chosen switching surfaces. This paper develops a control strategy to minimize the effects of the unmatched uncertainty upon the dynamic performance prescribed by the switching surfaces. This is achieved for a subclass of the uncertainty class considered by previous authors. The practical application of the control strategy to the design of a stability augmentation system for a light aircraft is presented. For this problem an ideal performance is well known and it is desirable that these ideal dynamics are exhibited across a wide range of flight conditions without degradation.

Sliding-mode output feedback controller design using linear matrix inequalities

The problem of designing a sliding mode controller for uncertain MIMO dynamical systems with matched and unmatched uncertainties using only measured output signals is addressed. A design methodology based on LMIpsilas under a polytopic formulation is presented for the existence and reachability problems. The proposed controller is static in nature. The reaching and sliding motion are guaranteed despite the presence of both matched and unmatched uncertainties. A design study involving the lateral control of an aircraft is employed in order to illustrate the efficacy of the approach developed.