Preliminary Investigation on the Possible Adaptive Control of an Inverted Pendulum-type Electric Cart

Abstract

The model-based control of Classical Mechanical systems often has to cope with the problem of the lack of precise dynamic models. In the case of underactuated systems this problem is further burdened by the existence of strong nonlinearities, even in the form of dynamic singularities. The simultaneous existence of these problems does not promise successful application of the traditional robust control approaches that are based on a Linear Time-invariant (LTI) approximation of the model in the vicinity of some “working point” and the intensive use of the frequency domain. The relatively simple, strongly nonlinear Robust Variable Structure/Sliding Mode (VS/SM) controllers may produce undesirable chattering while the more sophisticated, Lyapunov function-based adaptive techniques may require complicated computations because the dynamic model of a relatively simple mechanical structure computationally may be quite complicated, especially when the system is driven by a Pulse Width Modulated (PWM), brushless electric DC motor that together with the mechanical components determines a relative order 3 control task yielding terms of order 0, 1, 2, and 3 time-derivatives of the state variables. The aim of the present paper is to investigate whether to what extent the calculation of these terms can be eliminated by the use of a simple, Fixed Point-iteration (FPI)-based adaptive controller that could be implemented by the use of an embedded micro-controller. The simulation results that belong to a certain solution are promising.