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本文研究线性离散时间广义系统的最优预见控制器的设计问题.首先完善了关于线性离散时间广义系统最优调节理论的一个定理.然后将一阶前向差分算子作用在状态方程和可预见的目标值信号上,构造了包含可预见目标值信号的广义扩大误差系统,把跟踪问题转化为关于广义扩大误差系统的调节问题,并讨论了广义扩大误差系统的能稳性、因果能控性及因果能观性与原系统相应特性的关系.再利用因果能控性的特点,通过引入预反馈把问题转化为一个等价的广义因果系统的调节问题,对二次型性能指标函数进行改造,将问题转化为从广义扩大误差系统导出的正常系统的最优控制问题.最后利用前述最优调节理论的定理,得到了带有预见前馈补偿的最优预见控制器.为了便于应用,对所得到的理论给出了简明的实现步骤.数值仿真结果说明了理论结果的正确性和有效性.
In this paper, we study the design of the optimal predictive controller for a linear discrete-time generalized system. First, we perfect a theorem about the optimal regulation theory for a linear discrete-time generalized system. Then we apply the first-order forward difference operator to the state equation and predictable , A generalized extended error system containing predictable target value signals is constructed, and the tracking problem is transformed into the problem of the generalized extended error system. The stability, causality and controllability of the generalized extended error system And the relationship between causality and observability and the corresponding characteristics of the original system.Then, by using the characteristics of causality controllability, this paper transformed the quadratic performance index function by introducing the problem of pre-feedback into an equivalent adjustment problem of generalized causal system , The problem is transformed into the optimal control problem of the normal system derived from the generalized extended error system.Finally, the optimal predictive controller with predictive feedforward compensation is obtained by using the theorem of the optimal regulation theory.For the sake of convenience, The obtained theory gives concise implementation steps.The numerical simulation results show that the theoretical results are correct and effective .