LQ Optimal Multivariable PID Control Design for Skid-to-Turn Missile Autopilot

A multi-input multi-output (MIMO) proportional-integral-derivative (PID) compensation for pitch-roll-yaw integrated control of high angle of attack (AoA) skid-to-turn (STT) missile has been proposed. To this end, a relation between multivariable PID gains and state feedback gains is obtained for the system considered. The optimal state feedback gains are designed using linear quadratic regulator (LQR) approach. To find PID gains from above relation using a pseudo-inverse based approach which will guarantee desired performance, suitable LQR weights Q, R are choosen. For comparison, single-input single-output (SISO) PID controllers are also designed in each channel using LQR method. Simulations are carried out with MIMO as well as SISO PID designs. It is shown that due to high channel interaction, SISO design fails and proposed MIMO design yields satisfactory results. The performance and robustness are also studied through different frequency response plots.