A novel discrete PID+ controller applied to higher order/time delayed nonlinear systems with practical implementation

Abstract

This paper develops a novel approach for discrete time proportional integral derivative (PID) control, namely PID+, with application to manipulator arm with four-degrees of freedom. The approach utilizes extra proportional and input compensators to counteract the influence of the discrete time transfer functions higher than second order and having samples time delay more than unity, respectively. These plus compensators allow the exploiting of the full state feedback signals to construct the state variable feedback control law for the proposed PID+ controller. The work introduces two tuning approaches for the compensators of the novel PID+ controller; they are the Linear Quadratic (LQ) cost function by exploiting the non-minimal state space, namely the novel NMSS-PID+ form, and the pole placement. Simulation results verify the applicability of the proposed PID+ controller. Both tuning approaches, PID+/LQ and PID+/pole placement, show satisfactory steady state response with good control action, along with deadbeat response when applying the pole placement approach, in simulation. Finally, the paper shows successful practical implementation for the PID+ controller, when applied to the four degrees of freedom manipulator arm, for which all the control design criteria (tracking with acceptable response time, and input/output disturbance rejection) are met.