Optimized $\mathscr{H}_{\infty}$ Control for 2-DoF Helicopter Using Adaptive PSO and LMI

This paper presents an optimized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{H}_{\infty}$</tex> control for a two degree of freedom (2-DoF) helicopter based on Linear Matrix Inequalities (LMI) and Adaptive Particle Swarm Optimization (APSO). The 2-DoF helicopter is used as a laboratory helicopter model. The nonlinear dynamic equations of the system are obtained using the Euler-Lagrange equations. The integral action is introduced to minimize the static errors. A feedforward gain is used to eliminate the effect of the gravity disturbance. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{H}_{\infty}$</tex> criterion is employed to reject the effect of external disturbances. Based on a quadratic candidate Lyapunov function, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{H}_{\infty}$</tex> stability conditions of the closed loop system are formulated into an LMI. The optimal weighting matrix of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{H}_{\infty}$</tex> - LMI is derived using APSO. A comparative assessment on the system performance is investigated between regular integral-LQR, integral-LQR-APSO and the proposed controller.