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PID CONTROL Mechanical Engineering Experiment II

Department of Mechanical Engineering Faculty of Engineering Khon Kaen University Khon Kaen, THAILAND



Ideal System

Desired Output

Desired output not equal to setpoint

Not quite ideal because...

Desired output too slow Desired output oscillates Page 2





Desired Output

Desired output is measured and processed by a controller

The controller compares the desired output to the setpoint level to determine a new control input for the system

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PID CONTROL Proportional term Proportional gain (tuning parameter) Error (setpoint – output) time or instantaneous time Integral term Integral gain (tuning parameter) Dummy integration variable Derivative term Derivative gain (tuning parameter)

Proportional Term (P)

Integral Term (I)

- Directly make changes to the current error - Multiply the error by a constant Kp - High proportional gain yields large change in output - Too high proportional gain yields unstable system - Too small proportional gain yields less responsive controller

- Sum the error over time - Give the accumulated offset that should have been corrected previously - Multiply the accumilated error by a constant Ki - Accelerate the controller output towards setpoint - Eliminate the residual steady-state error produced by the proportional term

Derivative Term (D) - Calculate the slope of the error over time - Multiply the rate of change of the error by a constant Kd - Reduce the magnitude of the overshoot produced by the integral term - Is sensitive to noise in the error term

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PID CONTROL Why using PID control? Proportional term shows “PRESENT” Integral term shows “PAST” Derivative term shows “FUTURE” So “PRESENT” + “PAST” + “FUTURE”

P Characteristics

I Characteristics

D Characteristics

Larger value yields faster response

Larger value eliminates steady-state erros quickly

Larger value reduces overshoot but gives slow reponse and is sensitive to noise

Too large value yields instability and osciallations

Too large value yields overshooting

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FEEDBACK RESPONSE Parameters Overshoot - Maximum error between input and output - Percent overshoot = (Maximum overshoot / Desired value) x 100% Time delay (Td) - Initial time response until 50% of the output Rise time (Tr) - Time response between 10% to 90% of the output Settle time (Ts) - Initial time until the oscillation is within 5%

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PID CONTROL LABORATORY Objectives 1. To understand how a closed loop system works 2. To understand how a PID controller works 3. To understand the behaviors of each term (P, I, and D) 4. To understand the relationship among the terms (P + I, P + D, I + D, P + I + D)

Tasks Week 1 You are required to design a closed loop system (PID) to control the position of the given servo motor. Week 2 You are required to carry out an experiment of your closed loop system design. The laboratory report must be written and submitted to before week 3. Week 3 You are required to take the laboratory oral exam and your laboratory report will be commented.

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REFERENCES 1. PID Controller. Wikipedia. 2. CONTROL SYSTEMS, ROBOTICS, AND AUTOMATION - Vol. II - PID Control - Araki M. 3.

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PID Control