Desired dynamic equational proportional‐integral‐derivative controller design based on probabilistic robustness

Abstract

Uncertainties existing in industrial processes always result in many challenges for controller design. To enhance the ability of the closed-loop system to handle the uncertainties, a desired dynamic equational (DDE) proportional-integral-derivative (PID) controller is designed based on probabilistic robustness (PR) in this article. The necessity of the proposed design method is demonstrated by introducing the problem formulation. Based on its fundamentals, DDE PID designed based on PR (DDE-PR PID) is proposed for uncertain systems and corresponding design procedure is summarized as a flow chart. Then the proposed DDE-PR PID is designed for several typical processes and simulation results indicate that the proposed DDE-PR PID cannot only achieve satisfactory control performance for nominal systems, but also satisfy control requirements for all uncertain systems with the maximum probability.Finally, the proposed DDE-PR PID is applied to the nonlinear model of a fluidized bed combustor unit and the level system of a water tank. Its superiority in robustness is validated by both simulations and experiments, which shows the promising prospect of DDE-PR PID in future power industry. On the other hand, the DDE method is extended to the generalized two-degree-of-freedom PID controller and its bandwidth-parameterization is proposed in this article as well.

A Controller Synthesis Method to Achieve Independent Reference Tracking Performance and Disturbance Rejection Performance

“…SIMC and AMIGO are simple tuning methods that offer highly effective quantitative calculations, so they are regarded as better choices for PID tuning in engineering. 39 Table 3 lists the parameters of different controllers. Note that AMIGO PID has the same structure as DDE PID, as shown in Figure 1 .…”

“…In terms of practical systems, PID controllers are rarely used for the reason that the derivative action may lead to the self-oscillations of the control signal when measurement noise exists. 39 As a result, PI controllers are usually applied to industrial process control. In Section 6 , all controllers are designed based on PI controllers.…”

“…To demonstrate the merits of the proposed FC-DDE PI/PID in reference tracking and disturbance rejection, PID controllers based on the Skogestad IMC (SIMC) method, , approximated MIGO (AMIGO) method, and conventional DDE method , are selected as comparative controllers. SIMC and AMIGO are simple tuning methods that offer highly effective quantitative calculations, so they are regarded as better choices for PID tuning in engineering Table lists the parameters of different controllers.…”

“…Therefore, the proposed controller is designed for the level control system of a water tank. In terms of practical systems, PID controllers are rarely used for the reason that the derivative action may lead to the self-oscillations of the control signal when measurement noise exists . As a result, PI controllers are usually applied to industrial process control.…”

Special issue on PID control in the information age: Theoretical advances and applications

“…Shi et al 11 considered a so‐called dynamic equational PID controller, which augments the derivative control in the PID controller to high‐order differentials. The scheme is applied to the control of uncertain systems with possible parameter variations in bounded intervals, and the system robustness is evaluated in a probabilistic sense.…”