PID controller tuning for desired closed-loop responses for SISO systems using impulse response

Most of the proportional-integral-derivative (PID) controller tuning methods reported in literature are based on the approximate plant models (FOPDT or SOPDT models) derived from the step response of the plant. In this paper, a new method of designing PID controllers using ‘impulse response’ instead of ‘step response’ of the plant is presented. Treating the impulse response of the plant as a statistical distribution, the ‘mean’ and the ‘variance’ of the distribution are calculated and used in the calculation of PID controller parameters. Thus, the proposed method requires no approximation of the plant by any model. In this paper, a direct synthesis approach to PID controller design is proposed that makes use of Maclaurin series of the desired closed-loop transfer function, truncated up to the first three terms. PID controller parameters are synthesized to match the closed-loop response of the plant to the desired closed-loop response. Formulae for the calculation of PID controller tuning parameters are derived for the desired closed-loop response models of the types FOPDT and SOPDT. Only stable SISO systems are considered. The PID controllers tuned result in closed-loop responses very close to the desired response and perform equally well compared to other tuning methods reported in literature.