Abstract
SummaryProportional Integral Derivative (PID) controllers still represent the core control method for achieving output regulation of either linear or nonlinear systems in the majority of industrial applications. However, conventional PID control cannot guarantee specific state constraint requirements for the plant, when the system introduces uncertainties. In this paper, a novel nonlinear PID control that achieves output regulation and guarantees a desired state limitation below a given value for a wide class of nonlinear systems with constant uncertainties is proposed. Using nonlinear ultimate boundedness theory, it is shown that the proposed state‐limiting PID (sl‐PID) control maintains a given bound for the desired system states at all times, ie, even during transients, whereas an analytic method for selecting the controller gains is also presented to ensure closed‐loop system stability and convergence at the desired equilibrium. Two nonlinear engineering examples that include an electric motor and a dc/dc converter are investigated using the conventional PID and the proposed sl‐PID to validate the superiority of the proposed controller in achieving the desired output regulation with a given bounded state requirement.
Highlights
Since its first design in the early 1900s, Proportional Integral Derivative (PID) control has been dominating the engineering industry when it is desired to achieve both asymptotic regulation and disturbance rejection
Nazrulla and Khalil[8] have proposed a robust nonlinear integral controller, based on high-gain observers, capable of stabilizing nonminimum phase dynamics with a desired output regulation, whereas in the work of Ma and Khalil,[9] the output feedback controller tracks references generated from an external source without using an internal model
For the proposed state-limiting PID (sl-PID), the controller gains can be computed according to the analysis presented in the previous subsection leading to kP = 8, kI = 85, and kD = 0.01
Summary
Since its first design in the early 1900s, Proportional Integral Derivative (PID) control has been dominating the engineering industry when it is desired to achieve both asymptotic regulation and disturbance rejection. Techniques such as model predictive control (MPC),[27] for an excellent survey on its different properties, include the constraints into their formulation and aim to exploit the behavior of the system around the constraints These methods, present limitations in their implementation because they require the solution of an optimization problem online. For nonlinear systems with continuous-time dynamics, the output regulation problem with guaranteed state limitation using the well-understood and widely applied PID control and without modifying the control concept is still an open problem. The proposed sl-PID can replace the conventional PID control in applications where a state limitation is required, whereas the framework for selecting the controller gains presented in this paper can lead to a simple and effective design and implementation.
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