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受控对象的数学模型可用如下随机差分方程描述A(z~(-1))Y(t)=z~(-k)B(z~(-1))U(t)+C(z~(-1))w(t).(1)这里,A(z~(-1)),B(z~(-1)),C(z~(-1))均为z~(-1)的n_A,n_B,n_C阶多项式,z~(-1)为后向移位算子,U(t),Y(t),w(t)分别为系统的输入、输出和随机干扰序列,k为延迟. 为了解决非最小相位系统的伺服、跟踪控制和最优控制,Clarke提出了广义最小方差自校正控制,但正如Athans、李训经等所阐述的那样,对跟踪参考信号的最优控制问题,不能随便地选择目标泛函.分析广义最小方差控制方案,可以发现,为了使闭环系统稳定,性能指标(这里E为数学期望算子)
The mathematical model of the controlled object can be described as follows: () () () (-1)) w (t) (1) where A (z -1), B (z -1) and C (z -1) 1) is the polynomial of n_A, n_B, n_C and z -1 is the backward shift operator. U (t), Y (t) and w (t) are the input, output and random disturbance sequences , and k is delay. To solve the servo, tracking control and optimal control of non-minimum phase system, Clarke proposed generalized minimum variance self-tuning control. However, as explained by Athans and Li Xunjing et al., the optimal control of tracking reference signal Problem, we can not choose the objective functional conveniently.Analysis of the generalized minimum variance control scheme, we can find that in order to stabilize the closed-loop system, the performance index (where E is the mathematical expectation operator)