Abstract
The standard control performance assessment methods are based on the minimum-variance (MV) principle or modifications of it. The key point is that the MV benchmark (as a reference performance bound) can be estimated from routine operating data without additional experiments, provided that the system delay is known or can be estimated with sufficient accuracy. The main focus of the chapter is on presenting assessment methods based on minimum-variance control (MVC) for single feedback control and for combined feedback and feedforward control loops. The extension of MV assessment to the assessment of set-point tracking and cascade control is also provided. All methods presented are illustrated using many examples.
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Notes
- 1.
Following Ljung (1999), q is chosen as an argument of the polynomials rather than q −1 (which perhaps would be more natural in view of the right side) in order to be in formal agreement with z-transform and Fourier-transform expressions.
- 2.
For discrete systems with no time delay, there is a minimum one-sample delay because the output depends on the previous input, i.e. τ=1.
- 3.
One should here remember the linear correlation test used for the validation of identified linear models; see Sect. 2.3.
- 4.
The basic MVC is designed to solve regulation problems, where the objective is to compensate for stochastic disturbances and not to follow a reference trajectory. However, MVC can be extended to include variations in the reference, as described below.
- 5.
Remaining error terms are ignored here for simplicity.
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Jelali, M. (2013). Assessment Based on Minimum-Variance Principles. In: Control Performance Management in Industrial Automation. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-4546-2_2
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