Yoshifumi Okuyama

Robust Stability Evaluation of Sampled-Data Control Systems with a Sector Nonlinearity

Abstract This paper describes a robust stability evaluation of sampled-data control systems containing a sector nonlinearity in the forward path. The result of this paper is derived from the norm condition in the frequency domain by extending the Popovs criterion theory. Some lemmas are presented, a theorem for l 2 -stability is proved, and the stability margin (allowable sector) of a nonlinear element is explicitly exhibited. This theorem is valid only for classes of nonlinear sampled-data control systems that satisfy some of assumptions. A theorem for the validity of extended Aizermans conjecture is also presented. Some numerical examples are given to illustrate these results.

Amplitude dependent analysis and stabilization for nonlinear sampled-data control systems

This paper analyzes the amplitude dependent behavior of nonlinear sampled-data control systems in a frequency domain. We apply the robust stability condition for discrete-time nonlinear systems to a sampled-data control system containing a single nonlinear element in the forward path. By considering a restricted area (a sector) in the nonlinear characteristic, we can accurately predict and estimate the existence of a sustained oscillation whether it is periodic or not. In this paper, first, we summarize the robust stability condition and discuss the possibility of the amplitude dependent analysis for these types of nonlinear control systems. Then, we present a method of improvement in the stability for nonlinear sampled-data control systems.

Discrete-Time Model Reference Feedback and PID Control for Interval Plants

Abstract The physical parameters of controlled systems (plants) are uncertain and are accompanied by nonlinearity. The transfer function of the controlled system should, therefore, be expressed by interval polynomials. This paper describes the realization of robust control for that type of plant via discrete-time model reference feedback, and discusses the relationship between the feedback structure and the conventional (discrete-time) PID control system. Robust performance of the feedback control system is evaluated by using a discrimination method of characterisitic (dominant) roots area on a 2-plane. In this paper, we will present designing examples of a robust control system via model reference feedback which corresponds to a high-gain feedback and a kind of PID control.

Discretized PID Control and Robust Stabilization for Continuous Plants

This paper describes discrete-time and discrete-value (discretized/quantized) PID control and robust stabilization for continuous plants. Although all control systems are currently realized using discretized signals, the analysis and design of such nonlinear discrete-time control systems has not been elucidated. In this paper, the robust stability analysis of discrete-time and discrete-value (digital) control systems that accompany discretizing units at the input and output sides of a nonlinear element is performed in the frequency domain, and a method for achieving PID control and robust stabilization for nonlinear discretized systems on a grid pattern in the time and control variables space is presented. In the design procedure, a modified Nichols diagram and parameter specifications are applied. Numerical examples are provided to verify the validity of the designing method.

AMPLITUDE DEPENDENT ANALYSIS AND STABILIZATION FOR NONLINEAR SAMPLED-DATA CONTROL SYSTEMS

Abstract The robust stability condition for sampled-data control systems with a sector nonlinearity was presented in our previous paper. Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system can belong to this type of class. This paper analyzes the amplitude dependent behavior of nonlinear sampled-data (i.e., discrete-time) control systems in a frequency domain. First, the robust stability condition which was derived in our previous papers is applied to a sampled-data system containing a single time-invariant nonlinear element. Then, an instability condition for that type of nonlinear feedback system is derived. By considering restricted areas (two sectors) in the nonlinear characterisitic, the existence of a sustained oscillation is estimated (whether it is periodic or not), and the relationship between the stable (unstable) conditions and the result which is derived from the classic describing function is compared. Based on these considerations, the stabilization of nonlinear discrete-time control systems is examined in the frequency domain.

On the Robust Stabilization of Sampled-Data Control Systems with a Sector Nonlinearity

Abstract In this paper, we have described an evaluation method of the robust stability of sampled-data control syrstems with one time-invariant nonlinear element in the forward path and the possibility of the robust sta.biliza.tion of this tyrpe of control system. Stability theory involves the expansion of Popovs criterion to discrete-time systems and judgement by explicitly expressing criterion in the frequency domain. The nonlinear characteristics that should be considered need not be specially menloryless, but the summation of trapezoidaJ areas determined by the path of sampling points should be non-negative. In order to verify the above theory, we considered a broken line nonlinearity as a numerical example and the deterioration in the stability of nonlinear sa.mpleddata control systems caused by an increase in the sampling period. Improvement in the robust stability is possible not only by the phase lead effect by a linear compensator, but also byr a slight gain change within the sector.

On Sturm's theorem for interval polynomials

The number of characteristic roots in a specified contour on an s-plane can be determined by Sturms theorem. In this paper, we will analyze the sequential operations of coefficients based on the division algorithm when the characteristic equation is expressed as an interval polynomial. We will examine whether these operations are reduced to the extreme point results of interval coefficients, give a graphical interpretation of the discrimination method, and give some numerical examples.

Discriminance of characteristic roots area for interval systems

Abstract This paper describes the existing area of characteristic roots for control systems which are expressed by transfer functions that are composed of interval polynomials. A discrimination method of the number of characteristic roots in a specified area on an s-plane was developed, when a characteristic equation was expressed as an interval polynomial. This paper analyzes an invariance problem of dynamic characteristics such that the dominant roots do not break away from a specified circular area, and presents a discrimination algorithm (i.e., a division algorithm) for the extreme points of the uncertain coefficients. Designing examples of a control system which has a robust performance such that the location of the dominant roots does not vary excessively, as well as numerical examples for the discrimination method, are presented.

Model-Reference Discretized PID Control and Robust Stabilization for Continuous Plants

Abstract This paper deals with a designing problem of discrete-time and discrete-value (discretized) control systems based on a model-reference feedback structure. The model used in this study is assumed to be a second-order lag system that is expressed by a bilinear transformation. That type of discretized (nonlinear) control systems is presented and analyzed. The model reference feedback using a second-order continuous-value (linear) system is equivalently transformed into a traditional PID control. The robust stability analysis and design of such nonlinear control systems is examined in a frequency domain. Numerical examples for model-reference type discretized control are provided to verify the design method.

Robust stability evaluation of sampled-data control systems with time-invariant nonlinearity in a gain-phase plane

Describes a graphical evaluation of the robust stability in the frequency domain based on the results from our previous paper (1996) in which the extension of Popovs criterion to discrete-time systems was expressed in an explicit form. The control system described herein is a sampled-data control system with one time-invariant nonlinear element (sector nonlinearity) in the forward path. Considering the application to computer-aided control system design (CACSD), we present an evaluation method of the robust stability in connection with the size of sector nonlinearity and the gain margin on a gain-phase diagram (i.e. a modified Nichols chart). We show two results as numerical examples: one is where Aizermans conjecture was approved, and the other is where it was not.