Stability characteristics of a nonlinear direct current servo with proportional, integral, derivative controller: comparison with simulation and experimentation

The stability characteristics of a rotational position feedback system consisting of a digital proportional, integral, derivative controller, direct current motor and inertia load are presented. The system model incorporates digital-to-analog converter saturation and motor friction deadzone nonlinearities. The feedback system is analyzed for stability using both state-space Lyapunov techniques and frequency domain describing functions. Experimental and simulation results indicate the possibility of both stable and unstable limit cycles, depending on system parameters. The choice of state variables leads to a way of explaining the observed sticking action of the servo due to deadzone friction.