Improved Control Design Methods for Proximate Time-Optimal Servomechanisms

It is well known that minimum time-optimal control for servomechanisms can generate chattering in the presence of measurement noises, feedback delays, or model uncertainties; thus, it is not practical in applications. Maybe, the most popular alternative approach is the so-called proximate time-optimal servomechanism (PTOS). This approach starts with a near-time-optimal controller and, then, switches to a linear controller when the system output is close to a given target. However, the chattering problem is avoided at the expense of a slower time response. In this paper, two methods for eliminating the conservatism present in the PTOS are proposed. The first method applies a dynamically damped controller that allows the so-called acceleration discount factor to be pushed arbitrarily close to 1. The second method applies a continuous nonlinear control law that makes use of no switching. Experimental results show that the proposed designs practically eliminate the conservatism in the traditional PTOS.