Design of optimal PD control gains for a TORA: dominant pole assignment

In this paper, a new example of applying Routh-Hurwitz stability criterion is provided to design an optimal PD control gains for stabilizing a TORA. We solve analytically an optimization problem, which achieves a fast control response of the TORA. We present two steps to solve the optimization problem analytically. First, we perform a coordinate transformation to the TORA´s characteristic equation, and prove its unstability. Second, we design the optimal control gains which assign the unstable poles to the imaginary-axis by using the Routh-Hurwitz criterion. By using these two steps, we provide the optimal control gains and show that the closed-loop system consisting of the TORA and the PD controller has two pairs of complex-conjugate poles with the same real part. We verify the validity of the analytical result by comparing with numerical computation and numerical simulation.