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Output Feedback

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Most slides from Control Bootcamp by Prof. Steve Brunton and Control of Mobile Robots by Prof. Magnus Egerstedt

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Plant G (or System)

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Open Loop Control

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Open Loop Control

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Closed Loop Control (= Negative Feedback Control)

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Closed Loop Control

  • Feedback controller
    • Use of feedback with sufficiently high gain provides an approximate solution to the tracking problem even in the presence of system uncertainty and disturbance

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Transfer Function for Closed Loop System

  • Feedback changes the system transfer function
    • Change system dynamics
    • Change poles and zeros
    • Might change system stability

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Transfer Function for Closed Loop System

  • Feedback changes the system transfer function
    • Change system dynamics
    • Change poles and zeros
    • Might change system stability

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Transfer Function for Closed Loop System

  • Example 1

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  • Example 2

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Visualize Feedback

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Visualize Feedback

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Visualize Feedback

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Visualize Feedback

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Visualize Feedback

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Open Loop vs. Closed Loop

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Open Loop vs. Closed Loop

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Open Loop

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Closed Loop

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Closed Loop

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Model Uncertainty of Open Loop

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Model Uncertainty of Open Loop

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Model Uncertainty of Open Loop

  • Discrepancy from model uncertainty

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  • Stability
    • The open loop system cannot change the poles of system

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  • Uncertainty, Low Robustness
    • Predicting models incorrectly has a critical impact on speed

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  • Disturbance rejection
    • Disturbance directly affects the system

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Model Uncertainty of Closed Loop

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Model Uncertainty of Closed Loop

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PID Control

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Car Model

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P Control

  • The proportional term produces an output value that is proportional to the current error value.
    • Small error yields small control signals
    • Nice and smooth
    • So-called proportional regulation (P regulator)

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Model Uncertainty

  • Caveat: the "real" model is augmented to include a wind resistance term:

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  • At steady-state

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PI Control

  • The integral controller is the sum of the instantaneous error over time and gives the accumulated offset that should have been corrected previously
    • Stability
    • Tracking
    • Robustness

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PID Control

  • PID: by far the most used low-level controller
    • P: contributes to stability, medium-rate responsiveness
    • I: tracking and disturbance rejection, slow-rate responsive, may cause oscillations
    • D: fast-rate responsiveness, sensitive to noise

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  • Feedback has a remarkable ability to fight uncertainty in model parameters !

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PID Control

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PID Gains

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PID Gains

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PID Gains

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PID Gains

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General Tips for Designing a PID Controller

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MKC System as Closed Loop

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MKC System as Closed Loop

  • Mass

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MKC System as Closed Loop

  • Mass and spring

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MKC System as Closed Loop

  • Mass and spring

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MKC System as Closed Loop

  • Mass, spring and damper

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MKC System as Closed Loop

  • Mass, spring and damper

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