Design and Implementation of Two-Degree-of-Freedom Nonlinear PID Controller for a Nonlinear Process

Abstract

A Two-Degree-of-Freedom (2-DOF) Nonlinear PID (NPID) controller is designed for a conical tank level process. The process is modeled using black box identification method as a First Order Process with Dead Time (FOPDT) model. Two nonlinear first order tracking differentiators are designed for the nonlinear PID controller. The closed loop control is implemented for a wide operating range of the process with the designed controller. The implementation and simulation is carried out using Mat-lab Simulink software. The online implementation of proposed controller shows that 2-DOF NPID is better than 1-DOF NPID. Index Terms: Two-Degree-of-Freedom, First order process with dead time, Nonlinear PID, Nonlinear tracking differentiator I. Introduction A conical tank level process is a nonlinear process due to the conical shape of the tank. The change in area of the conical tank for equal rise in level is nonlinear. The nonlinear process is modeled as piecewise linear models at some operating points. This inherent nonlinear behavior of the processes makes control of such processes more complex. Presence of the nonlinearity in the plant often causes degraded performance of the overall process. A nonlinear PID controller is developed by defining a nonlinear function which gives the controller settings depending upon the calculated error and some tuning parameters (1)(2). A nonlinear function may contain number of parameters and values of those should be decided by the designer and it varies from plant to plant. When the process and the controller both exhibit nonlinear characters, a 2-DOF control scheme is considered to improve servo and regulatory problems (3). In the 2-DOF control scheme the closed loop transfer functions for servo and regulatory can be adjusted independently (4)(5)(6). In this work, the tuning of 2-DOF nonlinear PID controller is demonstrated to achieve stability and desired performance measures. This paper is organized such that first the design of the 2-DOF nonlinear PID control structure using the nonlinear tracking differentiators and secondly conical tank level process is described. Then the simulation study and online implementation of designed controller with actual process are shown. e when e e when e e sign e f p p p p p          