System Controls

Mechanical Engineering
System Dynamics and Controls

Bono
PID Controls and Two-Degrees-of-Freedom Control SystemsIntroduction

In today’s industrial company’s controllers utilize PID or modified PID control schemes. By using PID controllers and two-degrees-of-freedom configuration, we design control systems thatsatisfy two independent requirements. We will see a computational approach to the design of control systems. The approach can be used to design both single-degree of freedom and multiple degrees offreedom control systems. This two forms of approach are very popular in the industry.

Tuning rules PID controllers

If a mathematical model of the plant can be derived, then it is possible to applyvarious design techniques for determining parameters of the controller that will meet the transient and steady-state specifications of the closed-loop system. The process of selecting the controllerparameters is known as controller tuning. Ziegler and Nichols proposed rules to determining values of the proportional gain Kp, integral time Ti, and derivative time Td based on the transient responseof a given plant. Ziegler- Nichols rules, which are briefly presented in the following picture:

* First method – we can obtain experimentally the response of the plant to a unit-step input.This method applies of the response to a step input exhibits an S-shape curve. The S-shape curve may be characterized by two constants, delay time “L” and time constant “T”. The delay time and timeconstant are determined by drawing a tangent line at the inflection point of the S-shaped curve.

Ziegler-Nichols Tuning Rule Based on Step Response of Plant
(First Method)

The transfer functionC(s)/U(s) may then be approximated by a first-order system with a transport lag:

Notice that the PID controller tuned by the first method of Ziegler-Nichols rules give:

* Second method – We...