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A New Constructive Characterization of Stabilizing PID Controllers
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DOI：10.1109/ACCESS.2024.3415015.png)
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摘要
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In this paper, we present a new complete and constructive characterization of all the stabilizing regions in the PID gain space. It is based on D-partition theory and the fact that for a given proportional gain k(p) the stability boundaries in the plane of integral and derivative gains are all straight lines. Actually, we present the notion of the critical k(p) point, which is defined in the sense that the topology of the D-partition of (k(i), k(d)) plane can change when the k(p) crosses a critical $k(p) point. Moreover, we identify seven types of critical k(p) points and provide formulas for their computation. With the availability of all critical k(p) points, the stabilizing k(p) intervals can be exhaustively and exactly determined. By sweeping the k(p) parameter over the stabilizing k(p) intervals, the whole set of stabilizing PID controllers for a given plant is created. In addition, it allows for an efficient test of the existence of a stabilizing PID controller set without sweeping the $k_{p}$ parameter. To validate the newly presented analytical and constructive characterization of stabilizing PID controller sets and demonstrate the existence of seven types of critical k(p) points, five examples are provided.
Keyword:
Stabilizing PID controller set
D-partition theory
parametric-space method
stability domain
期刊
IF:
3.6
论文数:
9.8W
被引数:
29.4W
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