The integration of advanced linear parameter-varying and classical proportional–integral–derivative control methods has attracted great attention in control of nonlinear dynamic systems. However, linear parameter-varying proportional–integral–derivative control synthesis is a nonconvex bilinear matrix inequality problem. Although the synthesis conditions can be convexified in the case of proportional–integral control, a strong constraint on the structure of matrix variables usually leads to infeasible solutions. In this paper, a linear parameter-varying proportional–integral control design method is proposed to remove that constraint. The approach is based on the assumption of state-feedback proportional–integral control to guarantee the linear matrix inequality variables to be full matrices instead of block diagonal matrices, and extended linear matrix inequalities are proposed to synthesize the controller. This increases the likelihood of finding feasible linear matrix inequality solutions and reduces the conservatism. The proposed method is applied to control longitudinal and lateral dynamics of an F-16 aircraft and promising simulation results are obtained.

Switching control methods have great potential applications in flight control system design. However, nonsmooth control commands at switching instants could lead to performance degradations or bring in safety risks. This paper presents a smooth switching proportional-integral-derivative (PID) control method for linear parameter-varying (LPV) systems to solve this issue. By introducing a transition parameter subspace between any two neighboring LPV subsystems, the switched controller gains are designed to be smoothly varied when the parameter trajectory passes through these subspaces, and the Lyapunov function in the transition subspace is designed independently to make the algorithm less conservatism. The controller synthesis condition is formulated as a linear matrix inequality (LMI) optimization problem using Finsler’s lemma. The concept of average dwell-time (ADT) is employed to analyze the performance of the resulting closed-loop system. The effectiveness of the ADT-based smooth switching control strategy is demonstrated by applying it to the nonlinear longitudinal model of the F-16 aircraft, and the simulation results are compared with the traditional ADT switching control method. The results show that the proposed method can achieve a better transition performance with a simpler control structure.

An aeroservoelastic system can be described as a gridding-based linear parameter-varying (LPV) model, whose dynamic characteristics usually vary with the airspeed. Due to the high order of the system, it is necessary to perform order reduction on LPV models to overcome the control design challenges. However, when directly extending linear time-invariant (LTI) model order reduction technologies to the LPV system, states of the reduced-order LTI models generated separately at different grid points could be inconsistent. In this paper, a novel modal matching algorithm is proposed to solve the problem of state inconsistency by identifying the internal connection between the models at adjacent grid points. An oblique projection-based distance metric is defined to improve the reliability of the modal matching algorithm. The reduced-order LPV model constructed based on this method would have a high fidelity relative to the original model and a smooth interpolation performance between grid points. The proposed algorithm is applied to the X-56A aircraft, and numerical results show its effectiveness.