Parametric optimization for mixed H₂/H_∞ optimal PID controller of a flexible aircraft

Generally, a flexible aircraft's controller is designed based on a reduced-order model. But there are reduction errors due to model reduction, so it is needed to design a controller with strong robustness. In order to solve the problem, mixed H₂/H_∞ optimal PID controller parametric optimization was studied based on a reduced-order model of a flexible aircraft with 12-order. Firstly, the balanced truncation reduction method was employed to get a reduced-order model with 6-order. Secondly, the suitable robust weighting functions were selected based on the model reduction errors in frequency domain. And then, in order to compute the H₂/H_∞ performance index, a simplified computation method of H₂ norm of system errors was proposed. At last, a difference evolution algorithm was employed to optimize the parameters of the mixed H₂/H_∞ optimal PID controller. Simulation results indicated that the order of the mixed H₂/H_∞ optimal PID controller can stabilize the parameter and non-parameter uncertainties simultaneously. The stabilization of elastic structure deformation and the control requirement of rigid modes were also accomplished effectively.