1 / 35

Feedback Control

Feedback Control. A Simple Abstraction. An open loop control system Goal/desired state. Process output. Desired output. Process input. Controller. The process Under control. Open Loop Control . Only for static environment Accurate manipulation needed Problem:

emilia
Download Presentation

Feedback Control

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Feedback Control

  2. A Simple Abstraction • An open loop control system • Goal/desired state Process output Desired output Process input Controller The process Under control

  3. Open Loop Control • Only for static environment • Accurate manipulation needed • Problem: • Noisy environment (disturbance) • Inaccurate effector Disturbance Desired output Process output Process input Controller The process Under control

  4. Open Loop Control • May use expected disturbance • Static environment Predicted disturbance Disturbance Desired output Process input Process output Controller The process Under control

  5. Examples • Putting book on a desk • Activating an event • Start a sensor • Play a sound • Conduct a scripted movement • Question: What about inserting a light bulb?

  6. Desired output Process input Process output Controller The process Under control Feed Forward Control • Disturbance measured on the fly • Problems? • May not include all the parameters Measured disturbance Disturbance Sensors

  7. Feedback Control (Closed Loop) • Include all the parameters as included into the output. Disturbance Desired output Process output Process input Controller The process Under control Sensors

  8. Feedback Control • Another diagram Desired output Process output Process input Controller The process Under control Σ + - Sensors

  9. Example

  10. Errors • Direction (sign) • Magnitude (distance) • Frequent feedback is needed • Sensor rates can effect response • Control may not be immediate • May be a delay from when you decide to change, and when a change actually occurs!

  11. A Wall Following Robot • How would you use feedback control to implement a wall-following behavior in a robot? • What sensors would you use? • Would they provide magnitude and direction of the error? • What will this robot's behavior look like?

  12. Oscillation and the Set Point • Desired state is called the set point • Can we decrease oscillation? • A range rather than a single value • Slower change • Wall following example: • Larger turning angle • A range rather than fix distance

  13. Sensor Noise • What happens when there is sensor noise in the system? • Example: • Sensor tells the robot it is far from a wall, when it is close? • vice versa? • How might we fix these problems?

  14. Control Theory • Studies the behavior of control systems • Major basic controllers: • P: proportional control • PD: proportional derivative control • PID: proportional integral derivative control

  15. P: Proportional Control • Error = measurement – setpoint • Setpoint = desired output • Process input = Gain * error + bias • bias: manual reset (to fix any offset) Desired output Process output Process input Controller The process Under control Σ + - Sensors

  16. P: Proportional Control • Q: What happens if the gain is increased? • A: Loop may go unstable • Q: What if the gain is decreased? • A: It takes along time to get close enough to the setpoint. • Determining the gain: hard problem • analytically (mathematics) • empirically (trial and error)

  17. Setting Gain • Determining the gain depends on the physics of the system: • Analytical approaches: • System should be understood well • System should be characterized mathematically. • Trial and error (ad hoc, system-specific): • System should be tested extensively. • Can be done • manually • Automatically by the system • Wrong gain may put the system into oscillation!

  18. Oscillation • Wrong gain may put the system into oscillation

  19. Damping • The process of systematically decreasing oscillation • Properly damped: Reduces and removes oscillation in a reasonable amount of time.

  20. P: Proportional Control • Q: What happens if the system is very dynamic? • Example: Following another robot • A: P control does not work well. • It senses the present time. • Q: What happens close to the setpoint? • A: • If gain is fixed: May not work for low errors • Leaves some offset • If gain is high: Tends to overshoot

  21. Example Kp = 20 Kp = 50 Kp = 200 Kp = 500

  22. Example: Analysis overshoot steady-state error ss error -- difference from the system’s desired value settling time overshoot -- % of final value exceeded at first oscillation rise time -- time to span from 10% to 90% of the final value settling time -- time to reach within 2% of the final value rise time

  23. D: Derivative Control • Predict the future: • Adjust based on the rate of change • The speed of change • Example: wall following robot • High derivative: Very fast toward the wall • Low derivative: Very slow toward the wall • Output: • o = Kd * di/dt

  24. Momentum of Correction • Momentum of correction results in oscillation and instability • A result of a slow reaction time to the controller • Momentum = mass * velocity • D to overcome oscillation • Output = error * Gp + d(error)/dt * Gk • Example: Wall following: P and D are opposite each other • PD: Mostly used for industrial plants

  25. PD Control Kd = 3 Kd = 300 Kd = 30

  26. Integral Control • The controller output is proportional to the amount of time the error is present. • Integrate all previous values. • To overcome (eliminate) the offset • The longer the offset hangs around, the larger the I component becomes • Output o = Kf * int i(t)dt

  27. Example: PI • SS error (offset) has been removed Ki = 0 Ki = 2

  28. PI Example: Draw backs Ki = 20 Ki = 200 Ki = 90

  29. PID Controller • Proportional Integral Derivative Control is a combination of proportional, integral, and derivative control: • output = Kp * i + Kd * di/dt + Kf * int i(t) dt

  30. PID Controller

  31. PID results Kp = 100 Ki = 200 Kd = 2 Kd = 5 Kd = 10 Kd = 20

  32. Simulation http://newton.ex.ac.uk/cgi-bin/metaform?http://newton.ex.ac.uk/teaching/CDHW/Feedback/OvSimForm-gen.html

  33. Choosing Parameters Ziegler-Nichols Method • Adjust the set-point value, Ts, to a typical value for the system and turn off the derivative and integral actions (0). Select a safe value for the maximum power M and set the proportional gain to minimum. • Progressively increase the gain until suddenly decreasing or increasing Ts by about 5% induces oscillations that are just self-sustaining. • Call the gain at this stage Gu, and the period of the oscillations tu. Note the values of each quantity. • Set the controller parameters as follows: • P-Control: P=0.50*Gu, I=0, D=0. • PI-Control: P=0.45*Gu, I=1.2/tu, D=0. • PID-Control: P=0.60*Gu, I=2/tu, D=tu/8.   • Check the overall performance of system is satisfactory under all normal conditions.

  34. Is it Set Well? How do we measure system accuracy? • Elementary: The plant didn’t blow up • Informal: • Optimum decay ratio (1/4 wave decay) • Minimum Overshoot • Maximum Disturbance Rejection

  35. Is it Set Well? • Mathematical: • Various integral definitions, such as: • IAE - Integral of absolute value of error • ISE - Integral of error squared • Mostly reserved for “academic” purposes

More Related