Discrete-time simplified adaptive control algorithm and its application to a motor control

Abstract

Abstmct --Simplified adaptive control (SAC) is origiually proposed for the class of plant which satisfies almost strictly positive real (ASPR) condition. There have been two main methods t o circumvent this condition. One is t o add parallel feedforward compensation t o an original plant resulting in n new augmented plant which satisffes t h e ASPR condition. T h e other is t o contrive t h e signal in parameter adjustment law which is a linear cornbinatiori of o u t p u t error and control law. One of t h e authors has proposed a discrete-time algorithm which belongs t o t h e former. I n this paper, a new discrete-time algorithm is proposed which belongs t o t h e latter. This algorithm can reduce t h e o u t p u t e r r o r between plant a n d model to b e bounded and moreover t o zero if t h e steady s t a t e gain of t h e plant is kept constant under parameter variation. T h e stability of the algorithm is proved by using a Eyapunov function. This algorithm is applied t o the position control of a DC servomotor. Experimental results illustrate satisfactory performance even if its load is largely changed.

Classical and Simple Adaptive Control for Nonminimum Phase Autopilot Design

“…With this notation we geṫ K I (t) = e y r T I (20) where I is the resulting matrical adaptation coefficient for the combined gain K I (t).…”

Direct Adaptive Feedback Design for Linear Discrete‐time Uncertain Systems

“…, k ≥ 1. Substituting (9) into (8) and applying the fact that tr xy T = y T x, where n y ∈ and n x ∈ are column vectors, we obtain (11) and incorporate (11) into (10), yielding…”

“…However, available results were not Lyapunov-based techniques or Lyapunov-related results. For example, the MIT rule [5], the discrete-time adaptive stabilization algorithm [6], the parameter estimation scheme [7], the so-called simple adaptive control method [8,9], and the robust direct discrete adaptive control method [10] do not provide a valid Lyapunov candidate such that the stability hypothesis of [11] can be directly applied. Nevertheless, the synthesis and stability analysis of discrete event systems in [11,12] and the algebraic results given in [10,13] motivate us to apply Lyapunov concepts in the discrete-time adaptive feedback control scheme.…”

On Direct Adaptive Control for Uncertain Dynamical Systems - Synthesis and Applications

“…An ARMARKOV model for MIMO uncertain systems achieved adaptive disturbance rejection and traction (Venugopal & Bernstein, 1999). In addition, Shibata et al proposed a simplified adaptive control scheme based on Lyapunov analysis while the system satisfies the so called almost strictly positive real (ASPR) condition (Shibata et al, 1996). Bar-Kana (Bar-Kana, 1989) also used ASPR assumption and presented a robust discrete-time adaptive algorithm subjected to the condition of BIBO and the boundedness of the residual term.…”