Abstract
In this paper, we discuss an improved version of the conventional PID (Proportional–Integral–Derivative) controller, the Dynamically Updated PID (DUPID) controller. The DUPID is a control solution which preserves the advantages of the PID controller and tends to improve them by introducing a quadratic error model in the PID control structure. The quadratic error model is constructed over a window of past error points. The objective is to use the model to give the conventional PID controller the awareness needed to battle the effects caused by the variation of the parameters. The quality of the predictions that the model is able to deliver depends on the appropriate selection of data used for its construction. In this regard, the paper discusses two algorithms, named 1D (one dimensional) and 2D (two dimensional) DUPID. Appropriate to their names, the former selects data based on one coordinate, whereas the latter selects the data based on two coordinates. Both these versions of the DUPID controller are compared to the conventional PID controller with respect to their capabilities of controlling a Continuous Stirred Tank Reactor (CSTR) system with varying parameters in three different scenarios. As a quantifying measure of the control performance, the integral of absolute error (IAE) metric is used. The results from the performed simulations indicated that the two versions of the DUPID controller improved the control performance of the conventional PID controller in all scenarios.
Highlights
To date, the PID (Proportional–Integral–Derivative) controller is the most widely used controller in industry
The control performances of the 1D and 2D Dynamically Updated PID (DUPID) controllers are compared against a benchmark PID controller
The DUPID controller is constructed based on the assumption that the parameters in the plant vary with time in a smooth and gradual fashion
Summary
The PID (Proportional–Integral–Derivative) controller is the most widely used controller in industry. The discussed robust tuning methods have proven effective in improving the robustness in a variety of control systems They have certain downsides, and some of them are pinpointed as follows: firstly, in the tuning process it is necessary to account for all the parameters that can possibly vary and the bounds of their variation in advance; secondly, they usually need one or multiple linearized models of the nonlinear plant to design the controller; lastly, the methods based on optimization techniques come with a high computational burden as the optimization problem therein is non-convex. To tackle some of the aforementioned problems, in this paper we discuss a simple and computationally non-intensive, hands-on control algorithm which is an upgraded version of the conventional PID controller—a dynamically updated PID (DUPID) control scheme [17] This control approach uses a local quadratic model [18,19], of the plant control error to improve the robustness of the conventional PID against the change of the plant parameters.
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