Approximate H8 loop shaping in PID parameter adaptation

作者：Tsakalis Kostas S^*; Dash Sachi

来源：International Journal of Adaptive Control and Signal Processing, 2013, 27(1-2): 136-152.

DOI：10.1002/acs.2350

• PID tuning
• frequency loop shaping
• uncertainty bounds
• H8 estimation
• direct adaptation

This paper discusses the use of H-infinity approximation for the online adaptation of PID controller parameters. For a frequency loop-shaping control objective, it is possible to adapt the PID parameters directly with linear model estimation algorithms. Standard least squares algorithms are common solutions for this problem, but their estimates exhibit a well-known strong dependence on the properties of the excitation. This drawback becomes more pronounced for systems where the modeling mismatch is large, as is frequently the case in PID control. In an alternative formulation of the estimation problem, we use a filter-bank to decompose the error signal to different components and minimize approximately the H-infinity norm of the sensitivity-weighted error operator. This approach results in a more consistent estimate of the optimal PID parameters, at the expense of higher excitation requirements. It also allows for the computation of a health indicator to describe the confidence in the estimated parameters. The practical implication of this observation is that PIDs can be tuned more reliably, even in cases of large mismatch between the target and the feasible loop shapes. It also suggests a general theme where a minmax optimization of an operator error provides an advantage over signal error optimization. The key aspects of the algorithm are illustrated by numerical examples.

• 出版日期2013-2