EML 4314C

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EML 4314C

• Exam 2 Review

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Topics

• PID Tuning
• Lab 7 Synthesizing controller gains to meet
  system performance specifications (e.g., OS,
  steady-state error, stable, )
• Ziegler-Nichols (Z-N)
• Pole Placement
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, z, ?n, ?d and L01
• Logarithmic decrement

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PID Tuning

• Effects of P, I, D and velocity feedback on
  system response and the error
• Design procedure
• General approach
• Ziegler Nichols (Z-N)
• Z-N oscillation method
• Z-N reaction curve based method
• Pole Placement

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General Tips for Designing a PID Controller

• Obtain an open-loop response and determine what
  needs to be improved
• Add a proportional control to improve the rise
  time
• Add a derivative control to improve the overshoot
  
• Add an integral control to eliminate the
  steady-state error
• Adjust each of Kp, Ki, and Kd until you obtain a
  desired overall response.

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Ziegler Nichols PID Tuning (Oscillation Method)

• Start with a pure proportional controller and run
  a step test with a low value of Kp.
• Repeat the test by increasing (or decreasing) Kp
  until a stable oscillation begins to occur
  (oscillations with a constant amplitude). This
  value of Kp is called the ultimate gain, Ku.
• Note oscillation should be detected at the
  controller output.
• Determine Ku and Pc ? Kp , Ki and Kd
• Then touch up

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Ziegler-Nichols Reaction Curve Based Method

• A linearized quantitative version of a simple
  plant can be obtained with an open loop
  experiment, using the following procedure

1. With the plant in open loop, take the plant
manually to a normal operating point. Say that
the plant output settles at y(t) y0 for a
constant plant input u(t) u0. 2. At an initial
time, t0, apply a step change to the plant
input, from u0 to u8 (this should be in the range
of 10 to 20 of full scale).


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Ziegler-Nichols Reaction Curve Based Method
3. Record the plant output until it settles to
the new operating point. Assume you obtain the
curve shown on the next slide. This curve is
known as the process reaction curve. In Figure,
m.s.t. stands for maximum slope
tangent. 4. Compute the parameter model as follows
For plant model
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Figure Plant step response
Ziegler-Nichols Reaction Curve Based Method

• The suggested parameters are shown in Table.
• (on next slide)

process reaction curve
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Table Ziegler-Nichols tuning using the reaction
curve
Ziegler-Nichols Reaction Curve Based Method
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Pole Placement Approach
Based on 1st and 2nd order approximations
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Topics

• PID Tuning
• Lab 7 Synthesizing controller gains to meet
  system performance specifications (e.g., OS,
  steady-state error, stable, )
• Ziegler-Nichols (Z-N)
• Pole Placement
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, z, c, ?n, ?d and L01
• Logarithmic decrement

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Parameter Identification
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Parameter Identification
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Parameter Identification

• we can measure the frequency that will give us

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Parameter Identification

• L01 can be obtained from the data as the steady
  state position
• (x1(t1)-L01) and (x1(tn)-L01) can be measured
• solve for ?

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Parameter Identification

• add a known mass ?m to the car and obtain ?2 and
  then ?n2

• use a large ?m so ?n and ?n2 will differ enough
  so that any error in measuring the frequencies
  will not significantly impact the calculations
• Lastly, determine c for
• the two cases from ?