Control Systems

1
Control Systems
Welcome to
ME30029 / ME50151
Chapter 6. Root Locus Design

• Dr. M. Necip SahinkayaDepartment of Mechanical
  Engineering
• University of Bath

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Compensator Configurations
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Compensator Designs

• Adding and Cancelling Poles and Zeros
• PD (Lead) Compensation
• PI (Lag) Compensation
• PID (Lead-Lag) Compensation
• Empirical Tuning
• Ziegler-Nichols Method

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Addition of poles
Moves the root locus to the right
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Addition of zeros
Moves the root locus to the left
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Effect of zero on the step response
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Same root locus different configs
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Pole Placement
Step Repsonse
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PD (Lead) Compensator
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Lead Compensator An Example

• Plant
• Overshoot lt 20
• Rise time lt 0.25 s
• This gives
• ? 0.5
• ?n7.2 rad/s
• i.e. pole at s-3.5j3.5v3

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Design of Lead Compensator contd
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Design of Lead Compensator contd
Steady State Errors

• Proportional Compensator
• Es1/K1
• Lead Compensator
• Esb/(Kda)0.029
• PD Compensator
• Es1/(Kda)0.024

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PI (Lag) Compensator
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PI (Lag) Compensator Example
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PID (Lead/Lag) Compensator
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Lead/Lag Compensator Example
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Steady-State Error to Unit Ramp
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Ziegler-Nichols Method 1
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Ziegler-Nichols Method 2

• Increase gain until oscillations start, and
  record it as K0
• Measure oscillation period, P
• Adjust the parameters as follows

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Ziegler-Nichols Example
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Ziegler-Nichols Example-contd
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Ziegler-Nichols Example-contd
Step response
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The End

• End of Chapter 6.
• gtgtRoot Locus Design

Thank you
Dr. M. Necip Sahinkaya Department of Mechanical
Engineering University of Bath