Showing papers on "Sliding mode control published in 1976"

On the exact model matching controller design

Abstract: The problem of designing a static state feedback controller which matches a given multivariable system to a desired ideal system (model) is treated. The system under control is assumed in state space form while the model is assumed in transfer matrix form. An algorithm is developed which separates the conditions which must be satisfied by the system under control and the model to be matched from the equations which must be solved to find the gains of the feedback controller. Two examples are included.

Optimal-aim control strategies applied to large-scale nonlinear regulation and tracking systems

Abstract: Several optimal-aim control strategies for large-scale nonlinear regulation and tracking systems are discussed. A theorem concerning explicit optimal-aim control laws with adaptive-feedback implementations, an example of its application to a transient power-system model, and a qualitative comparison of the optimal-aim strategy and a classical optimalcontrol strategy for a linear harmonic-oscillator model are given.

Continuous-time implementation of optimal-aim controls

Abstract: A modified optimal-aim control strategy for special classes of nonlinear systems is presented, and a theorem leading to an explicit, continuous-time implementation of the strategy is given.

The control of nonlinear econometric systems with unknown parameters

Abstract: An approximate solution, based on the method of dynamic programming, is provided for the optimal control of a system of nonlinear structural equations in econometrics with unknown parameters using a quadratic loss function. It generalizes the methods previously proposed by the author for the control of a nonlinear econometric model with constant parameters and of a linear econometric model with uncertain parameters. It is an improvement over the method of certainty equivalence which replaces the unknown parameters by their mathematical expectations and utilizes the solution for the resulting model. Since the solution is given in the form of feedback control equations, many of the useful concepts and techniques developed in the theory of optimal feedback control for linear systems are now applicable to the control of nonlinear systems using the method proposed, including the calculation of the expected loss of the system under control by analytical rather than Monte Carlo techniques. IN THIS PAPER, I present an approximate solution to the optimal control of a system of nonlinear structural equations using a quadratic welfare loss function when the parameters of the system are unknown. This is a generalization of ths solution given in Chapter 12 of Chow [2] for the control of nonlinear econometric systems with known parameters. It is also a generalization of the solution given in Chow [1] for the control of linear econometric systems with unknown parameters. The method of dynamic programming is applied to solve an optimal control problem involving a nonlinear econometric system with unknown parameters. As it turns out, the solution amounts to linearizing the nonlinear model about some nearly optimal control solution path and then applying a method for controlling the resulting linear model with uncertain parameters. This paper advances the state of the art in the control of nonlinear econometric systems as it improves upon the certainty-equivalence solution which is obtained by replacing the random parameters in a system by their mathematical expectations. It provides for a set of numerical feedback control equations based on a system of nonlinear structural equations in econometrics. It will show that many useful analytical concepts and tools developed in the theory of control of linear systems are indeed applicable to the control of nonlinear systems. Furthermore, in the derivation of an approximate solution using the method of dynamic programming, it will indicate precisely where the approximation takes place and why an exact solution is difficult to achieve. In Section 2, we set up the control problem and provide an exact solution to the optimal control problem for the last period. In Section 3, we give an approximate solution to the multiperiod control problem using dynamic programming. In Section 4, the mathematical expectations required in the solution of Section 3

Singular control test for optimal periodic control problems

Abstract: The singular control test which is useful for determining if the optimal periodic control is superior to the optimal steady control is presented in its general form Then the relation of the singular control test to the π-test which is known as a frequency domain approach is clarified

Design of servo for gyro test table using linear optimum control theory

Abstract: A control system is designed and implemented for a test table the motion of which is to track the output of a gyroscope. The process to be controlled is governed by a third-order differential equation with an important nonlinearity due to static friction. Representing the friction as an independent random walk yields a dynamic process amenable to design by methods of linear control theory. An existing design program was used to calculate the compensator transfer function which was realized with standard capacitors, resistors, and operational amplifiers. The compensator was installed in the test table and results in excellent closed-loop system performance.

Design of near-time-optimum rotation control procedures for a spinning symmetric satellite

Abstract: Near-time-optimum control procedures for the rotational motion of a spinning symmetric spacecraft are obtained with the aid of the Lyapunov stability theory It is shown in this correspondence that the near-optimum controls are simple to implement and that the performance loss can be limited by a suitable selection of system parameters Results have been obtained for satellites with constant and variable spin speed

On the comparison of optimal control systems

Abstract: This correspondence presents conditions which permit the comparison of the optimal performance of control systems which have the same criterion but different dynamics. These conditions are applied to linear quadratic problems and to establishing performance bounds for suboptimal systems.

Output Feedback Control of Servodamper System

Abstract: This paper presents a systematic design of servodamper systems from a point of view of output feedback control Firstly, by using a parameter optimization technique, the output feedback control law is derived In the case of incomplete feedback problems, however, the instability of the system must be considered in contrast to the optimal control system Secondly, this paper presents a new concept of "the best performance point", which minimizes the mean square value of a state Thirdly, in accordance with the best performance point, the determination of the output control law o f a servodamper system is demonstrated and the resulting system is compared with the optimal control system The experiment of the servodamper system subject to the application of the output feedback control law is also derived