Improvement of a Fixed Point Transformations and SVD-based Adaptive Controller - Tar, József K. (2019)
In this paper some refinement of a novel control approach is reported that fits to the “traditional line of thinking” according to which in the most practical cases neither very precise, nor even complete system model is needed for obtaining precise control for dynamical systems. The validity of this statement is briefly pointed out in the most popular approaches as the main idea of the “Robust Sliding Mode / Variable Structure Controllers”, in the Adaptive Inverse Dynamics and in the Slotine-Li Adaptive Controllers based on Lyapunov's 2nd Method, and in a recently published problem tackling using the simple geometric interpretation of the Singular Value Decomposition (SVD). In the present approach the originally proposed convergent, iterative Cauchy sequences are nonlinearly moderated to adaptively control a coupled nonlinear system, the cart plus double pendulum serving as popular paradigm of dynamicall not very well conditioned systems. It is shown that the proposed moderation removes the small sharp fluctuation in the control torque that inherently belonged to the original solution without significantly degrading the control quality. This statement is substantiated by simulation results.