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

This paper presents two new controllers and uses an extension of the generalized secant method of solving linear equations. 1] The rst controller is adaptive and operates in the time domain. The second one is a learning-adaptive controller which uses a similar mathematical concept, but it is formulated to deal with repetitive systems with repetitive disturbances. This controller operates in the repetition domain. For both controllers, the formulation of the systems into a linear estimation problem is presented as well as the solution using the secant method. A convergence is also given for both controllers. In addition, some practical modiications 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 non-linear systems, operating repetitively. Non-linearities of these dynamic systems have been ampliied by requiring them to follow a highly non-linear and demanding trajectory.