Abstract
Up to this point in the book, we have assumed that the plant model has been given, and the objective is to carry out system analysis and controller design. In many situation, however, a good model is not available. The two typical solutions to this problem are (i) to model the plant and identify the parameters and (ii) use an adaptive controller. In both cases certain plant sructural information is typically needed, such as the plant order, which may be available in simple cases but not readily so in more complicated situations. In this chapter we examine a more direct approach, wherein the goal is to design a controller for the plant without the intermediate step of obtaining a detailed model; it is a generalization of the classical approach to tuning a three-term PID controller used for single-input single-output systems. The method requires the plant to be stable and it assumes that (i) a finite number of experiments can be carried out on the plant, and (ii) it is possible to carry out on-line tuning of the controller parameters. While the method is presented for the case of step tracking, the approach can be generalized.
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Notes
- 1.
The classical way to tune a variable is to examine the step response and find the one which has the “nicest” step response; the problem is that everyones definition of “nicest” is different.
- 2.
We represent this by \(\Vert \hat{e} \Vert _2 := [ \int _0^{10} \Vert e ( t) \Vert _2^2 \, dt ] ^{1/2} \).
- 3.
In a practical situation, we would only be able to try a small number of choices of \({\varepsilon }\), many fewer than used here to create Fig. 4.3.
- 4.
We use \(k_1\) rather than \(K_1\) to emphasize the fact that it is a scalar.
- 5.
We represent this by \(\Vert \hat{e}_1 \Vert _2 := [ \int _0^{10} e_1 ( t) ^2 \, dt ] ^{1/2} \).
- 6.
We represent this by \(\Vert \hat{e}_2 \Vert _2 := [ \int _0^{30} e_2 ( t) ^2 \, dt ] ^{1/2} \).
- 7.
We represent this by \(\Vert \hat{e}_3 \Vert _2 := [ \int _0^{100} e_3 ( t) ^2 \, dt ] ^{1/2} \).
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Davison, E.J., Aghdam, A.G., Miller, D.E. (2020). On Tuning Regulators. In: Decentralized Control of Large-Scale Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6014-6_4
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