Abstract The paper considers the nonlinear optimal vibration control problem for systems with multiple delays, i.e. control delay, state delay, and measurement delay, under reference input. The time-delay system is transformed into an equivalent delay-free one via functional transformations. The nonlinear optimal control law is designed by solving a Riccati equation, a Sylvester equation, and an adjoint differential equation. The effects generated by nonlinearity and time-delay are compensated by the nonlinear compensator and the memory terms in the designed controller. An internal model is constructed so that the disturbance will be rejected with zero steady-state error as well as the reference is tracked, through the dynamical compensator produced from the internal model. An observer is constructed to make the controller physically realizable. The result is extended to vehicle suspension systems. It is demonstrated that the road vibration that is encountered by the suspension will be canceled entirely by the proposed control. Numerical simulations illustrate the effectiveness of the presented controller.

中文翻译：

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应用于车辆悬架的多时滞系统的非线性最优内模控制

摘要 研究了参考输入下多时滞系统的非线性最优振动控制问题，即控制时滞、状态时滞和测量时滞。时滞系统通过函数变换转化为等效的无时滞系统。通过求解 Riccati 方程、Sylvester 方程和伴随微分方程设计非线性最优控制律。非线性和时延产生的影响由非线性补偿器和设计控制器中的记忆项进行补偿。构建了一个内部模型，以便通过从内部模型产生的动态补偿器以零稳态误差拒绝干扰并跟踪参考。构造观察者以使控制器在物理上可实现。结果扩展到车辆悬架系统。结果表明，悬架遇到的道路振动将被建议的控制完全消除。数值模拟说明了所提出的控制器的有效性。