Pid Control of a Linear System

Abstract

The purpose of this lab was to understand the components of an open vs. closed loop system and understand components of a coupled tank. By interpreting and adjusting parameters of a Proportional, Integral, and Derivative (PID) control loop the lab allows us to achieve understand how to achieve a desired response. Also, we had a chance to review PID concepts learned in class when analyzing the coupled-tank system response and estimated system response utilizing the Ziegler-Nichols method of tuning, and manually adjusted portions of the PID controller to facilitate a desired response.

Objective

The PID control of a linear system lab focuses on the components of a coupled tank system and controllers. This lab provided the opportunity of being able to recognize the differences in components of an open loop vs. a closed loop system. It also emphasized the understanding of parameters used in a P, PI, and PID controller. Analysis was done focusing on how to calculate initial tuning values and how to adjust controller parameters until a desired response is achieved.

Introduction

In this lab, we examined the coupled tank system. The coupled tank system is a widely used engineering system across several different disciplines and industries of engineering and manufacturing. It is used in oil processing, salt water treatment plants, and paper plants. Coupled tanks use control algorithms to maintain fluids at the desired level. In our lab, we examined a system using a PID (Proportional, Integral, Derivative) control.

There are linear and nonlinear systems. In a linear system, the relationship between the input and the output is linear. For a linear system, a transfer function can be applied to model the ratio of the output to the input. However, most systems in the real world are non-linear. In a non-linear system, no transfer function can be applied. This requires us to make assumptions to linearize a system. Linearizing a system allow engineers to easily analyze a system. This lab focuses on a Closed-Control Loop system, namely, the PID controller. A closed loop system allows us to make adjustments to the system based on sensor feedback (in our case, a pressure sensor). A closed loop system is shown below:[pic 1]

Figure 1: Closed-Control Loop

Where:

                    Y(s) = Output after control parameters applied = G(s)U(s)                                                       (1)

E(s) = Ydesired(s) – Y(s) = Error Summation                                                                                     (2)

U(s) = C(s)E(s)                                                                                                                                   (3)

The PID controller, in the time domain can be modeled after the following equation:[pic 2]