PID controller document for controlling the motor, Study notes of Control Systems

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FEEDBACK CONTROL

SYSTEM

NED University of Engineering & Technology

LAB # 09

 Lab Experiment 11

 (^) Objective: Introduction to PID controller

• (^) Study the three term (PID) controller and its effects on the feedback loop response.
• (^) Investigate the characteristics of the each of proportional (P), the integral (I), and the derivative (D) controls, and
• (^) how to use them to obtain a desired response.

o (^) First, let's take a look at how the PID controller works in a closed-loop system using the schematic shown. o (^) The variable (e) represents the tracking error , the difference between the desired input value (R) and the actual output (Y). o (^) This error signal (e) will be sent to the PID controller , and o (^) the controller computes both the derivative and the

o (^) The signal (u) just past the controller is now equal to the proportional gain (KP) times the magnitude of the error plus the integral gain (KI) times the integral of the error plus the derivative gain (KD) times the derivative of the error.

Temperature Control System

Car Driving System

o (^) The three-term controller: The transfer function of the PID controller looks like the following: o (^) KP = Proportional gain o (^) KI = Integral gain o (^) KD = Derivative gain

o (^) Suppose we have a simple mass, spring, and damper problem. o (^) The transfer function between the displacement X(s) and the input F(s) then becomes:

Example Problem:

 (^) Open-loop step response: Let's first view the open-loop step response. num=1; den=[1 10 20]; plant=tf(num,den); step(plant) MATLAB command window should give you the plot shown below.

Proportional control:

o (^) The closed-loop transfer function of the above system with a proportional controller is: et the proportional gain (KP) equal 300 :

Kp=300; contr=Kp; sys_cl=feedback(contr*plant,1); %by default –ve feedback put 1 and for positive feedback + t=0:0.01:2; step(sys_cl,t)

Proportional control:

roportional-Derivative control:

o (^) The closed-loop transfer function of the given system with a PD controller is: t K P equal 300 as before and let K D equal 10.

Kp=300; Kd=10; contr=tf([Kd Kp],1); sys_cl=feedback(contr*plant,1); t=0:0.01:2; step(sys_cl,t)

roportional-Derivative control: