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一阶加纯延时模型难以精确描述被控对象,因此传统的PID控制器不能取得满意的控制效果。基于精确的高阶模型提出了一种最优PID控制器的设计方法。利用广义Hermite-Biehler定理获得使闭环系统稳定的PID控制器集合。在该PID控制器集合中,运用遗传算法寻找基于ITAE指标最优的PID控制器参数。利用广义Kharitonov定理及Monte-Carlo随机试验方法对PID控制器鲁棒性和性能鲁棒性进行评价。仿真结果表明:该文算法对高阶对象具有良好的控制性能,对模型的不确定因素具有较好的适应性和鲁棒性。从而证实了该文算法的有效性,可以应用于高阶系统的控制。
First-order plus pure delay model is difficult to accurately describe the controlled object, so the traditional PID controller can not achieve satisfactory control effect. Based on the accurate high-order model, a design method of optimal PID controller is proposed. A generalized Hermite-Biehler theorem is used to obtain a set of PID controllers that stabilize the closed-loop system. In the PID controller set, genetic algorithm is used to find the optimal PID controller parameters based on ITAE index. The generalized Kharitonov theorem and the Monte-Carlo random test method are used to evaluate the robustness and robustness of the PID controller. The simulation results show that the proposed algorithm has good control performance for high-order objects and has good adaptability and robustness to the uncertainties of the model. Thus the validity of the proposed algorithm is verified and it can be applied to the control of higher order systems.