Robustness evaluation and robust design for proportional-integral-plus control

Abstract

Proportional-integral-plus (PIP) control provides a logical extension to conventional two-or three-term (proportional-integral-derivative) industrial control, with additional dynamic feedback and input compensators introduced when the process has second order or higher dynamics, or time delays. Although PIP control has been applied in a range of engineering applications, evaluation of closed-loop robustness has generally relied on empirical methods. In the present article, expressions for the H ∞ norm of two commonly used PIP control implementations, the feedback and forward path forms, are used, for the first time, to quantify closed-loop robustness. It is shown that the forward path form is not robust for unstable plants. Additional expressions for the H ∞ norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the H ∞ norm are derived for the simplest plant, while simulation results based on numerical optimisation are provided for higher order examples. We show that, for certain plants, there are (non-unique) sets of PIP control gains that minimise the H ∞ norm. The H 2 norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the H ∞ norm is used as a design parameter for a practical example, namely control of airflow in a 2 m by 1 m by 1 m forced ventilation chamber. The performance of the new PIP H ∞ controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

Eigenvalue Analysis and Case Study Examples of Fractional Order Generalised Predictive Control

“…The latter cost function includes two scalar hyper-parameters, α and β, and the impact of these parameters has been investigated in this article. Of course, various different model-based design approaches can all produce the same outcome if the design criteria are set 'correctly' [23].…”

[Regular Paper] Stochastic Non-minimal State Space Control with Application to Automated Drug Delivery

“…The method is shown to be potentially very effective at reducing input variance but relies upon the system model and so potentially reduces the robustness of the closed-loop system. As a result, the authors are also investigating robust control and uncertainty in this context [30], [31].…”

Controlled homeodynamic concept using a conformable calculus in artificial biological systems

“…( 13) becomes where ϒ is the output of the system and χ β ( t ) is the conformable controller of order β. When β → 1, we have a controller modeled in Wilson et al [32] . This control models a simple cell, which we aim to minimize it.…”