New Adaptive and Learning-Adaptive Control Techniques Based on an Extension of the Generalized Secant Method

Abstract

This paper presents two new controllers and uses an extension of the generalized secant method of solving linear equations.1 The first controller is adaptive and operates in the time domain. The second one is a learning-adaptive controller which uses a similar technique to handle repetitive disturbances. This controller operates in the repetition domain. For both controllers, die formulation of the systems into a linear estimation problem is presented as well as the solution using the secant method. A proof of convergence is also given for both controllers. In addition, some practical modifications are presented to increase the robustness and stability of the systems. Furthermore, an analog network is proposed for increasing the speed of the controllers which is especially useful for the learning-adaptive controller since this network parallelizes most of the computation necessary for establishing the control, in hardware form. The adaptive controller is tested in simulations of two highly non-linear dynamic systems (a non-linear mass-spring-dashpot and a damped pendulum) against the performance of a self-tuning regulator and shows considerable superiority both in terms of speed of convergence and accuracy over the self-tuning regulator. The learning-adaptive controller also shows a great performance for controlling repetitive dynamic systems when applied to the same two nonlinear systems, operating repetitively. Non-linearities of these dynamic systems have been amplified by requiring them to follow a highly non-linear and demanding trajectory. © 1997 Taylor & Francis Group, LLC.