Optimizing Constrained Series PIDA Controller for Speed Loops Inspired by Ziegler-Nichols

The article presents a simplified optimization method of constrained series proportional-integral-derivativeacceleration (PIDA) controllers for the design of speed loops with a process approximated by an integral-plus-dead-time (IPDT) model. It was created by combining the analytical adjustment of the controller using the multiple real dominant pole (MRDP) method with the subsequent approximation of the complex conjugate controller zero with a double real pole/time constant. The optimal value of this time constant is determined by onedimensional numerical analysis using as performance measures the integral of absolute error (IAE) and monotonicity-based shape-related deviations calculated for setpoint and disturbance step responses of loops with constrained control signal. In contrast to the four-dimensional search of optimal values of cost functions used in the performance portrait method, the combined procedure enables a significant acceleration of calculations with possible refinement of the optimal solution.