Elimination of Initial undershoot of Non-minimum Phase System using Model Reference Adaptive Control

Initial undershoot is an unavoidable and undesirable common phenomenon in the step response of the Non-minimum phase (NMP) system and it creates difficulties in tracking control of the NMP system. Odd and even number of right half-plane (RHP) zeros of transfer function model of the NMP system produce initial undershoot and overshoot respectively and it creates an obstacle in the tracking control of the NMP system. To overcome these difficulties, the Lyapunov-based Model Reference Adaptive Control (MRAC) has been suggested here and the novelty of this technique is that it not only nullifies undershoots and overshoots, but it also tracks the reference input trajectory simultaneously. Different SISO NMP systems have been considered for the verification of suggested control methodology and one benchmark two input two output (TITO) NMP system has been considered to strengthen its claim on the elimination of unacceptable initial undershoot of the NMP system in MATLAB simulation environment.