R. V. Monopoli

Paper: Discrete model reference adaptive control with an augmented error signal

A method is developed for designing discrete model reference adaptive control systems when one has access to only the plants input and output signals. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Lyapunovs second method. The augmented error signal method is employed to ensure that the normally used true error signal approaches zero asymptotically without requiring anticipative values of the plant output signal. Such anticipative signals are replaced by others easily obtained from low pass digital filters operating on the plants input and output signals.

Adaptive control for systems with hard saturation

The augmented error signal concept, recently introduced, can be useful in designing model reference adaptive systems for plants with inputs which are subject to hard saturation. Liapunovs Direct Method is used as the basis for these designs. Figure 1 shows the configuration for the types of systems considered. The adaptive control acts to null the augmented error, and, in the process, also assures that the true error between plant and model approaches zero.

Improved convergence and increased flexibility in the design of model reference adaptive control systems

A modified Liapunov design technique for model reference adaptive control system is shown to result in improved system convergence. An adaptive rule, derived on the basis of a new Liapunov function, is compared to the previous rule. A local stability analysis applied to the modified design shows that the error response is more rapidly convergent. Furthermore, system simulations show that the transient response for the adjustable parameters is also improved. A second result presented is a design technique for a class of plants whose parameters cannot be adjusted directly. This design leads to a system with a set of prefilter and feedback adjustable gains as the adaptive parameters and physically realizable linear time-invariant filter networks in both the feedback and prefilter paths. It eliminates the problem of nonunique adaptive laws previously encountered and requires only n - m - 1 derivative networks for its implementation (nth order plant with m zeros); hence, if m = n - 1, no derivative networks are required for implementation. In order to maintain a bounded plant input signal, the zeros of the plant transfer function must be restricted to the open left-half plane.

Model Reference Adaptive Control, Estimation and Identification Using Only Input and Output Signals

Abstract Significant recent advances in the application of stability theory to the adaptive control and identification of systems, and adaptive state estimation are considered. Emphasis is on those methods which utilize only input and output measurements of the system, and do not require derivatives of the output signal.

Discrete Model Reference Adaptive Systems with Measurement Noise

Abstract A digital computer simulation study is presented for a class of discrete model reference adaptive systems designed using Lyapunov’s direct method. Plant output measurements are assumed to contain uniformly distributed additive noise. It is shown that the design works well even when such noise is relatively extreme. A new result is presented pertaining to improving the convergence properties of these systems. This result is obtained by modifying the dynamic characteristics of the augmented error equation.

Direct model reference adaptive control: Progress, problems, and prospects

In this paper an attempt is made to describe the progress to date, the problems, and the prospects for Direct Model Reference Adaptive Control Systems. The most significant progress has been in the development of the theory. Algorithms now exist which assure stable operation of the closed adaptive loop for both continuous time and discrete time systems. The most difficult problems remaining stem from the somewhat restrictive nature of the assumptions which must be made concerning the controlled system, and the fact that few hard results are available for the performance of the algorithms in the presence of measurement noise. In spite of these problems, the method has been successfully applied to some relatively simple systems. This fact, combined with recent progress in the theory, gives hope that the prospect of applying it to more complex systems is good.

Model reference adaptive control using only input aid output signals

It is shown how globally stable model reference adaptive control systems may be designed using only the plants input and output signals. Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Liapunovs direct method and the Meyer-Kalman-Yacubovich lemma. Filtered derivatives of the plant output replace pure derivatives which are normally required in these systems. An augmented error signal replaces the error previously used which is the difference between the model and plant outputs. However, global stability is assured in the sense that this difference approaches zero asymptotically.

Design of a multivariable model following adaptive control system

This paper presents an adaptive control system design for a multivariable plant. Based on Liapunovs direct method the resulting control system forces the plant outputs to track the outputs of an ideal model of the plant. Results presented include the design approach, its application to a two input-two output plant and data indicating the performance achieved when the control algorithm was tested by digital simulation.

A stable hybrid adaptive algorithm with periodic sampling and gain adjustment

In this article a hybrid algorithm for model reference adaptive control of single-input single output systems is presented. The control structure involves a continuous time as well as a discrete time part, instead of being all discrete or all continuous as in previous approaches. The system is sampled periodically at a frequency F, and knowledge of bounds on the plant parameters enables us to determine a bound F* such that the closed loop system is stable whenever F > F*.

Discrete Model Reference Adaptive Control with an Augmented Error Signal

Abstract In this paper a method for designing discrete model reference adaptive control systems when one has access to only the plant’s input and output signals, is given. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Liapunov’s second method. Anticipative values of the plant output are not required but are replaced by signals easily obtained from a low pass filter operating on the plant’s output. The augmented error signal method (introduced in [1] for continuous systems) is employed ensuring finally that the normally used error signal also approaches zero asymptotically.