Raymond A. DeCarlo

Variable structure control of nonlinear multivariable systems: a tutorial

The design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented. Using the Utkin-Drazenovic method of equivalent control and generalized Lyapunov stability concepts, the VSC design is described in a unified manner. Complications that arise due to multiple inputs are examined, and several approaches useful in overcoming them are developed. Recent developments are investigated, as is the kinship of VSC and the deterministic approach to the control of uncertain systems. All points are illustrated by numerical examples. The recent literature on VSC applications is surveyed. >

Perspectives and results on the stability and stabilizability of hybrid systems

This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear Systems

This paper considers a system consisting of a set of two unstable linear autonomous state models. Control is achieved by selecting which system to activate. The control objective is to quadratically stabilise the state trajectory by switching between the two unstable systems. Presuming the existence of a stable convex combination of the two unstable system matrices, three stabilising control strategies are discussed: time average control, a variable structure control, and a hybrid feedback control. Two examples are provided to illustrate the ideas in the paper.

Asymptotic stability of m-switched systems using Lyapunov functions

An investigation of asymptotic stability of m-switched systems based on Lyapunov functions is given. An m-switched system is a system x.=A/sub ik/x where A/sub ik/ in (A/sub 1/,. . .,A/sub m/) and i/sub k/ is an index from a switching sequence, i.e., control is achieved by switching between possible A/sub i/-matrices. The authors consider questions such as: existence of regions, called Omega -regions, where the m-switched system energy decreases as measured by Lyapunov functions associated with these regions; inclusion of one Omega -region by another; coverage of the state-space by the totality of these regions; and structural conditions on the time derivatives of the Lyapunov functions so that this state-space coverage can be accomplished. Answering these questions is necessary to satisfy a theorem and its associated conditions for asymptotic stability of an m-switched system.<<ETX>>

Construction of piecewise Lyapunov functions for stabilizing switched systems

This paper discusses the problem of stabilizing a pair of switched linear systems. A control law is developed using a Lyapunov function having a piecewise continuous derivative. A Lyapunov function yielding a stable switching rule is shown to exist as long as there exists a stable convex combination of the system matrices. The use of this stable combination for other control strategies is explored.<<ETX>>

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.

A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing

In this paper we present the development of (1) a sliding mode controller for stabilization of the rotational dynamics of a vertical shaft magnetic bearing in addition to providing tracking capabilities, and (2) a sliding mode observer for state and disturbance estimation. Rotor imbalance causes sinusoidal disturbances which necessitates robustness inherent in sliding mode observers and controllers. The sliding mode control design includes (1) the definition of an equilibrium manifold upon which the magnetic bearing has the desired stability and tracking properties, and (2) the control selection from one of several potential control strategies for driving the system to this manifold and maintaining it there. A sliding mode observer strategy is proposed to estimate derivatives of measured signals in the presence of unmatched disturbances by filtering discontinuous approximations of the derivatives. Simulation results demonstrate the utility and robustness of a sliding mode controller and observer for stabilizing the rotational dynamics of a magnetic bearing.

Development and Validation of a Battery Model Useful for Discharging and Charging Power Control and Lifetime Estimation

Accurate information on battery state-of-charge, expected battery lifetime, and expected battery cycle life is essential for many practical applications. In this paper, we develop a nonchemically based partially linearized (in battery power) input-output battery model, initially developed for lead-acid batteries in a hybrid electric vehicle. We show that with properly tuned parameter values, the model can be extended to different battery types, such as lithium-ion, nickel-metal hydride, and alkaline. The validation results of the model against measured data in terms of power and efficiency at different temperatures are then presented. The model is incorporated with the recovery effect for accurate lifetime estimation. The obtained lifetime estimation results using the proposed model are similar to the ones predicted by the Rakhmatov and Virudhula battery model on a given set of typical loads at room temperature. A possible incorporation of the cycling effect, which determines the battery cycle life, in terms of the maximum available energy approximated at charge/discharge nominal power level is also suggested. The usage of the proposed model is computationally inexpensive, hence implementable in many applications, such as low-power system design, real-time energy management in distributed sensor network, etc.

An overview of software cybernetics

Software cybernetics explores the interplay between software and control and is motivated by the fundamental question whether or not and how software behavior can be controlled. In this paper, we formulate the underlying motivations and ideas of software cybernetics and review various existing research topics in this emerging area, including feedback mechanisms in software processes, bisimulation and controllability, adaptive software, software synthesis, software test process control, and adaptive testing. We identify software rejuvenation and performance control, software fault-tolerance, logical foundation for control systems, and communication complexity for control systems as potential research topics. Several on-going research projects are also summarized.

A formal model of the software test process

A novel approach to model the system test phase of the software life cycle is presented. This approach is based on concepts and techniques from control theory and is useful in computing the effort required to reduce the number of errors and the schedule slippage under a changing process environment. Results from these computations are used, and possibly revised, at specific checkpoints in a feedback-control structure to meet the schedule and quality objectives. Two case studies were conducted to study the behavior of the proposed model. One study reported here uses data from a commercial project. The outcome from these two studies suggests that the proposed model might well be the first significant milestone along the road to a formal and practical theory of software process control.