期望指标集约束下一类随机系统的满意PID控制

研究一类随机系统具有期望的动态误差系数、稳态输出方差和相对稳定裕度约束的满意PID控制问题．首先应用满意控制思想，给出期望指标集的相容性定义；然后分别推导出PID控制器满足期望的稳定裕度指标的参数域边界解析式、满足期望的动态误差系数指标和期望的稳态输出方差指标的参数解集的解析式；最后给出期望指标的相容性判别方法以及相容性解集求取策略．通过算例验证了所提出方法的有效性．

On satisfactory PID control for a class of stochastic systems with desired index set constraints

The problem of satisfactory PID control for a class of stochastic systems with constraints on dynamic error coefficient, steady-state output variance and relative stability margin is considered. By using the idea of satisfactory control, the definition of the consistency of desired index set is proposed. The expression of describing the boundaries of PID controller parametric set satisfying the desired relative stability margin is derived. The analytical formulas describing the PID controller parameter sets satisfying the given dynamic error coefficient index and the desired steady- state output variance index are derived, respectively. The criterion to determine whether the given index is consistent with each other or not and the strategy of calculating the consistency set are given. A numerical example shows the validity of the proposed design method.