Design of stabilizing PI and PID controllers
Design of stabilizing PI and PID controllers
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DOI：
10.1080/00207720600783785
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发表时间：
2006-06
影响因子：
4.3
通讯作者：
N. Tan;D. Atherton
中科院分区：
文献类型：
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作者：
N. Tan;D. Atherton
本文给出了一种计算全部稳定PI控制器的新方法。所提出的方法是基于绘制的稳定边界轨迹（kp，ki）平面，然后计算的PI控制器的参数的稳定值为给定的控制系统。提出的方法不需要对参数进行扫描，也不需要线性规划来求解一组不等式。因此，它提供了几个重要的优势，在这个方向上获得的现有结果。所提出的方法也适用于计算所有的稳定PI控制器的多输入多输出（MIMO）控制系统考虑到两个输入两个输出（蒂托）系统使用解耦技术。除了稳定，该方法被用来计算所有的稳定PI控制器，实现用户指定的增益和相位裕度。此外，该方法被扩展到解决三参数PID控制器。对于kd的固定值，在（kp，kd）平面中获得稳定给定系统的PID控制器参数的极限值，对于ki的固定值，在（kp，kd）平面中获得稳定给定系统的PID控制器参数的极限值。然而，对于PID控制器的情况下，微分增益或积分增益上的网格需要用于计算所有稳定PID控制器。给出的例子来显示所提出的方法的好处。
In this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (kp , ki )-plane and then computing the stabilizing values of the parameters of a PI controller for a given control system. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus, it offers several important advantages over existing results obtained in this direction. The proposed method is also applied for computation of all stabilizing PI controllers for multi-input multi-output (MIMO) control systems with consideration given to two-input two-output (TITO) systems using decoupling technique. Beyond stabilization, the method is used to compute all stabilizing PI controllers which achieve user-specified gain and phase margins. Furthermore, the method is extended to tackle 3-parameters PID controllers. The limiting values of PID controller parameters which stabilize a given system are obtained in the (kp , ki )-plane for fixed values of kd and (kp , kd )-plane for fixed values of ki . However, for the case of PID controller, a grid on the derivative gain or integral gain is needed for computation of all stabilizing PID controllers. Examples are given to show the benefits of the method presented.