Showing papers on "Variable structure control published in 1990"

Robust output tracking for non-linear systems

Abstract: The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(∊), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control te...

Globally stable robust tracking of nonlinear systems using variable structure control and with an application to a robotic manipulator

Abstract: The globally stable robust output tracking for a class of nonlinear systems is considered. Based only on the knowledge of the bounds on the uncertainties, a variable structure control (VSC) law is developed under the structure matching assumption. It is shown that the outputs of the closed-loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop. All signals inside the loop are shown to be bounded for all time. To illustrate the efficiency of the controller, the approach is applied to the case of a two degree-of-freedom (DOF) robotic manipulator with variable payload. Numerical simulation results are also provided. >

VSS observer for linear time varying system

Abstract: The problem of designing an observer for state estimation using variable structure system (VSS) theory is discussed. The theory and design principles for linear time-varying systems are presented. The observer is constructed by introducing a block-observable from which is similar to a lower triangular matrix. The convergence of the observer is guaranteed by a sliding mode with first-order filter. Simulation results show that the proposed observer is able to provide correct estimated values of the states. >

A Comparative Study of a Luenberger Observer and Adaptive Observer-Based Variable Structure Speed Control System Using a Self-Controlled

Abstract: Abstmct-This paper presents an analysis of the state observer-based robust speed control of a self-controlled synchronous motor (SCSM) . A variable structure control (VSC) technique is utilized to achieve robust ( parameter-insensitive) characteristics. The speed and acceleration signals required for the implementation of the variable structure speed control (VSSC) are dynamically estimated with state observers. Two kinds of observers-the Luenberger full-order observer and an adaptive observer- are explored in this paper. The results obtained illustrate that Luenberger observers do not estimate the system states accurately when the system parameters vary. This inaccuracy in the state estimation results in a deteriorated performance of the VSSC. Therefore, the possibility of using an adaptive state observer (ASO) is investigated. As expected, the AS0 estimates the system parameters and the system states simultaneously, thus making VSSC possible. The design methods and the simulation results presented demonstrate the potential of the proposed scheme.

Near-Minimum Time, Closed-Loop Slewing of Flexible Spacecraft

Abstract: The near-minimum time single-axis slewing of a flexible spacecraft with simultaneous suppression of vibration of elastic modes is considered. The hyperbolic tangent (tahh) function is used as a smooth approximation to the discontinuous sgn function occurring in the rigid body "bang-bang" control. Variable structure control concepts are used to identify the necessary characteristics of the control switching line. Simulations of the rest-to-rest and tracking maneuvers indicate that the elastic energy can be reduced by several orders of magnitude with only a modest increase in the maneuver time. Introduction M ANY future large space structures, due to mass con- traints, will be flexible. For the purpose of analysis these systems can be modeled with a large number of modes of vibration. For certain applications, it will be desirable that such a spacecraft be able to slew as rapidly as possible, within the operating limits of the control actuators. The problem of control design for rotational maneuver and vibration suppres- sion of flexible spacecraft has been addressed extensively.1'10 Optimal control theory can be applied to enforce quiescent terminal conditions on the flexible modes, usually by applying a quadratic cost function that weights the control rates and the states. The order of the system model grows rapidly as the number of flexible modes to be controlled is increased, mak- ing it impractical to attempt to control more than a few flexible modes. Furthermore, there is no rigorous means by which control magnitude constraints may be enforced. Al- though a feedback method such as the linear quadratic regula- tor (LQR) with terminal constraints9"11 is attractive because it can enforce quiescent conditions oh the elastic modes, its computational complexity is burdensome. The optimal control solution to the minimum time, single- axis, rotational maneuver problem for a rigid body gives a control scheme characterized by saturation of the control throughout the maneuver with at most one control switch that is instantaneous (bang-bang). Although not exactly achiev- able in physical systems, and even though the trajectories are extremely sensitive to variations in spacecraft parameters, this control law has wide application for rigid systems using on-off thrusters. When rigorously applied to flexible systems, how- ever, the result is typically multiple control switches and excessive excitation of the flexible modes of vibration. Previ- ous investigations of the near-time optimal maneuver for flexible systems7'8 are open-loop designs requiring extensive computational effort. An alternative is to compute the re- quired parameters for a number of initial conditions off-line and use table lookup and interpolation for a particular ma- neuver. This may involve excessive storage. We start with the assumption that the minimum time solution for a rigid space- craft can serve as an initial approximation to the near-mini- mum time solution for a flexible structure. In other words, we

Newton, observers and nonlinear discrete-time control

Abstract: Development of exact asymptotic observers for nonlinear discrete-time systems is addressed. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that Newton's algorithm, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems. The utility of the observer for closed-loop, observer-based, feedback control is also established. Some non-local aspects of the results are also discussed. >

A new approach to position and contact force regulation in constrained robot systems

Abstract: A feedback control problem for regulation of contact force and position in constrained robot systems is considered. The nonlinear differential-algebraic equations which describe the dynamics of a constrained robot system are linearized about a constrained equilibrium. A method of obtaining an equivalent state realization for the resulting linear differential-algebraic equations is developed. This method is numerically efficient since it is based on a singular value decomposition. A linear quadratic optimal control problem associated with the linearized differential-algebraic equations is solved. The resulting linear feedback control law guarantees good regulation of both contact force and position of the constrained robot. Since the method is based on the linearization of the nonlinear differential-algebraic equations, it is valid only in a neighborhood about the point of linearization. Two robot examples are considered in order to illustrate the proposed method. >

Variable-structure control approach of decentralised model-reference adaptive systems

Abstract: In the paper, the problem of decentralised model-reference adaptive control, for linear time-varying large-scale systems, is investigated by using a variable-structure control approach. The global reaching condition of the sliding mode of a composite system is derived and a new scheme of decentralised control is proposed. This scheme can guarantee the stability of a sliding manifold of the composite system. Furthermore, a modified scheme is given which makes the weighted sum of the sliding manifold motions converge to the prospective speed. Finally, a numeral example is calculated.

Qualitative analysis and control of a DC-to-DC boost converter operating in discontinuous mode

Abstract: The boost cell operating in discontinuous conduction mode based on an approximate discrete-time difference equation is investigated. A qualitative discussion of the steady-state and open-loop dynamical behavior is presented. A linearized small-signal equation that leads to a linear feedforward control law for regulating this type of converter is derived. The conventional linear scheme provides satisfactory control in the neighborhood of the operating point, but ceases to meet the requirement as soon as the small-signal assumption is violated. A nonlinear feedforward control law whose validity extends over a wider range of fluctuation of the variables about the operating point is proposed, along with some simulation results that confirm the superiority of the proposed nonlinear control over its linear counterpart. >

Robust nonlinear control of robotic manipulators

Abstract: A robust nonlinear control strategy is proposed to deal with the control problem of robotic manipulators with second order nonlinear actuator dynamics. The control scheme is composed of two stages: the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage is aimed at exact linearization and input/output decoupling of the nonlinear actuator‐manipulator system in the task space by nonlinear feedback and nonlinear state space diffeomorphic transformations. The resulting closed‐loop nominal system is capable of precise trajectory following in a desired second‐order linear behavior. To compensate uncertainties in a practical situation, an optimal error correcting compensator is designed to achieve some robustness at the perturbed dynamics stage. Simulation study of a cylindrical robot is given to illustrate the effectiveness of the proposed scheme.

Robust variable structure control of model reference systems

Abstract: A variable structure control system (VSCS) yields total or selective invariance to system parameter variations and disturbances when in the sliding mode. In order to prescribe the system performance, a model-following approach to VSCS design is used. The required behaviour is achieved by defining a model with ideal response characteristics, and a VSCS is designed so that the error between the plant and the model is forced to exhibit a sliding mode. A parameter insensitive controller with improved disturbance rejection which achieves desired system performance results. The resulting nonlinear scheme cannot be assessed using conventional frequency domain techniques. A new analysis tool is therefore proposed and used to explore the robustness of such a nonlinear control scheme. The design technique is illustrated for lateral multimode control. The aircraft system requires a parameter insensitive control type with improved disturbance rejection if possible. In addition, the ability to prescribe flying quality requirements directly is important. The problem thus provides a suitable challenge for the technique. The robustness analysis is illustrated using the resulting VSCS applied to a range of realistic perturbation models of the fully nonlinear aircraft model.

Sliding mode-a new way to control series resonant converters

Abstract: The application of the theory of variable structure control systems for the control of resonant DC-DC converters is illustrated. The full-bridge configuration of series-resonant converters (SRCs) is used. The converter is operated at resonant frequency to obtain both output-to-input voltage characteristics similar to those of the buck converter and high efficiency. To arrive at an exact mathematical model, the SRC is viewed as a piecewise linear system. However, under some approximations and a suitably selected set of state variables, the SRC is characterized by a linear continuous-time model which allows determination of the equivalent control via the sliding mode control (SMC) theory. To obtain a sliding regime, the appropriate sliding surface is selected by assigning poles. This control law constitutes a new approach to the control of resonant DC-DC converters. >

An introduction to variable structure control

Abstract: In this introductory chapter attention will be focused upon the regulator, where the aim of the design is to regulate the system state to zero. Much of the theory may be applied with suitable modifications to model-following and tracking control systems. In this chapter some of the basic features and properties of variable structure control have been discussed. Numerous applications to a wide variety of practical problem are listed. The deterministic control of uncertain time-varying systems control is achieved using nonlinear feedback control functions, which operate effectively over a specified magnitude range of a class of system parameter variations, without the need for on-line identification of the values of the parameters. This control philosophy contrasts sharply with stochastic adaptive control systems in which the control law is altered whilst system parameter values are calculated using online identification algorithms.

Decentralized variable structure control for tracking in non-linear systems

Abstract: The problem of tracking time-varying trajectories in non-linear systems is considered. These trajectories could be generated on-line by a reference model. The problem is tackled by considering the overall system as a set of decentralized linear sub-systems which can be modelled as a set of double integrators and treating the non-linearities as uncertainties with known bounds on their magnitudes. A variable structure controller is designed based on the theory of uncertain dynamical systems. The system is shown to track a class of trajectories generated by the reference mode! (a set of double integrators) to within a specified tolerance. Some analysis is presented to explain the dynamic behaviour of the closed-loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty. Simulation results are presented to validate the conclusions.

Discrete time integral sliding mode control for discrete pulse modulated converters

Abstract: Sliding mode control for resonant link converters is introduced in a formal manner through a specific example of a buck resonant link DC-DC converter. The use of variable structure systems theory as a valuable tool to characterize the dynamic behavior of discrete pulse modulated systems in demonstrated. The suboptimal steady-state behavior of discrete pulse modulated converters under conventional control methods is brought out. The discrete time integral sliding mode control as an alternative control method with better performance attributes is proposed. It is demonstrated that the sliding mode control methods developed for the control of a PWM (pulse width modulation) power converter can be extended to the resonant link converter operating under discrete pulse modulation, and the performance can be improved by adding the integral-error term to the sliding surface. The conditions for sliding mode to exist under integral sliding control are obtained. All the results are verified by simulation, and experimental results confirming the concepts are presented. >

Applications of output feedback in variable structure control

Abstract: Most of the techniques for the design of Variable Structure Control Systems (VSCS) for both scalar and multivariable systems that is presented in the literature assumes that either the state vector is directly measurable or that an observer is used to reconstruct the state. In systems which do not have the full state vector available or that have a set of output measurements y, the usual technique for VSCS design of equivalent control cannot be applied. This chapter discusses the design of VSCS for the case of output feedback. This will be followed by a section extending the ideas to the output feedback case.

On Control System Described by a Class of Nonlinear Differential-Algebraic Equations: State Realization and Local Control

Abstract: A theoretical framework for the study of control systems defined by a class of nonlinear differential-algebraic equations is established. We first introduce the class of nonlinear control system considered, which is represented by a special but important class of nonlinear differential-algebraic equations. Assumptions are given for which the defining nonlinear differential-algebraic equations are well posed, in the sense that for given input and given consistent initial data, in a specified smooth manifold, there exists a unique smooth solution. A procedure for obtaining a local nonlinear state realization is developed; this realization can thus form the basis for control of the original differential-algebraic system. An approach for design of a linear feedback controller which achieves local regulation near an equilibrium solution is suggested. The framework established in this paper generalizes recent developments for control of mechanical systems with holonomic constraints and for control of mechanical systems with classical nonholonomic constraints.

Robust constrained motion control of multi-arm robots holding a common object

Abstract: A variable structure control (VSC) method is developed for robust constrained motion control of multiarm robots holding a common object in the presence of parametric uncertainties and external disturbances. By introducing a set of generalized coordinates, the closed-chain dynamic equation of robot system can be decomposed into position and force controlled subspace. In the controller design, position and force control are treated together and designed via VSC. For coordinating each robot, load distribution is carried out for minimizing weighted energy consumption. >