Optimal Discrete PI Controller Design for a DC-DC Boost Converter Fed PMDC Motor Drive System Using Constrained Optimization and Routh–Hurwitz Stability Analysis

In this paper, a design of an optimal discrete PI controller for a DC-DC boost converter that fed a PMDC motor drive system is presented. The small signal model (SSM) is extracted and validated theoretically and experimentally. The system transfer function has a right half plane zero (RHPZ) which adversely affects the frequency response, making the design of the closed-loop control challenging in terms of stability and dynamic performance. Therefore, stability analysis is performed to determine the stable operating region of the controller. To achieve optimal dynamic performance and robust stability, the PI controller parameters are optimized using a constrained optimization technique. Interior point algorithm (IPA) is employed and formulated based on a designed cost function combining integral of the time-weighted absolute error (ITAE) and normalized integral of the absolute control effort rate (IACER), while its constraints are selected according to the derived stability conditions. The developed optimal continuous-time controller is then discretized using the Tustin transformation method for real-time digital implementation. Experimental investigations are conducted under speed-reference tracking, sudden-load disturbance, and input-voltage variation conditions. Experimental results demonstrate that the designed controller achieves quick dynamic response, accurate speed regulation, effective load disturbance rejection, and robust stable operation under abrupt testing conditions.