Optimization of nth order square linear controller in the realm of describing function approach for nonlinear multivariable square system

In this paper, the procedure to optimize the gains of a nth order square linear controller with respect to nonlinear multivariable square system is established. The optimization is conducted in time domain and frequency domain for closed loop and open loop system respectively. The developed procedure is demonstrated on an unstable multivariable robot arm. The analysis results show that the optimization is successful and the transient response of the nonlinear closed loop system is able to be improved in terms of overshoot and settling time.