Study On Optimal Vibration Control For Time-Delay Systems With Application To Vechicle Suspension Systems

In this paper, firstly, the relative studies and results on the problem of optimal vibration control (OVC) for time-delay systems, nonlinear systems, and vibration control up to now are given in detail. Then the design of OVC law for time-delay systems and nonlinear time-delay systems are considered. The extence and uniqueness of the OVC law are studied and a suboptimal control law is given. The physical realization problem is discussed. The results are applied into simulations on suspension models to prove their effectiveness. The main contents are presented as follows.1. The approach named model transformation for time-delay systems is introduced. The time-delay systems are transformed into equivalent nondelayed systems in form. The optimal control law is derived by solving Riccati and Sylvester equations. And the effects produced by the delays are compensated by the control memory term.2. The theory of feedforward control is applied. For the disturbances with known dynamics and unknown initial conditions, the feedforward and feedback control law is designed, in which the feedforward control term compensates for the effects produce by disturbances. A reduced-order state observer is constructed to make the feedforward control physically realizable and solve the problem of unmeasured states.3. For the nonlinear time-delay systems, the model transformation and successive approximation approach (SAA) are extended to design the OVC law. The OVC law obtained consists of accurate linear feedback, feedforward terms, memory terms for time-delays, and a nonlinear compensation term which is the limit of the adjoint vector sequence. The former can be obtained by solving a Riccati equation and a Sylvester equation, and the latter can be got by solving the linear nonhomogeneous sequences using SAA. Using a finite-step iteration of the adjoint vector among optimal solution sequence, a suboptimal control law can be obtained.4. The designed control laws are applied to the numerical simulations on vibration control for suspension models. The state-space representations for a quarter-car model, a half-car model, and a full-car model are given based on their dynamical equations. The exosystems describing road vibrations are established. And the simulations results demonstrate the performances of car achive expected objectives and verify the effectiveness of desiged optimal control laws.