Feedback

1. Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo Feedback

2. Outline of Today’s Lecture Actuate Sense • Review • Class Policy • What is Control? • Feedback • Open Loop Systems • Closed Loop System • Positive Feedback • Negative Feedback • Control actions using feedback Compute

3. Class Policies • Syllabus • Students are expected to be at class on time. • Book: Online at • http://www.cds.caltech.edu/~murray/amwiki/index.php/Version_2.10e • You will be required to read this BEFORE coming to class. • Recitation points come from your reading! • Homework is due on the date shown in the syllabus at the beginning of the class period • Late homework will not be accepted • Neatness Counts! • Individual work • Academic dishonesty (cheating, plagiarizing, and related offenses,) will be harshly dealt with.

4. Control • Control = • Sensing + • {Where are you at? Is it where you want to be?} • Computation + • {Can you find a path to where you want to go?} • Actuation • { Make things happen to get you there!}

5. Why Controls? • Why Controls? • Things move • Too many things happening • Things move too fast for the human brain to compute and for muscles to act • Noise and disturbances • Accuracy and precision • Cost

6. Where Do You Find Controls? • Everywhere!

7. Controls: What are differences here? • Control = Sense + Compute + ActuateBench rest • TOW explained

8. Open Loop Control • Usually “set point” systems • Advantages • Simple • Sensitive to environment • Set and forget • Disadvantages • Non correcting • Sensitive to disturbances • Insensitive to environment • Examples • Irrigation systems • Washing machines Sensing Compute Actuate

9. Closed Loop Control Actuate Sense • Adds a feedback loop to the control system • For computational purposes, it is shown as Controller Plant Compute Sensor Disturbance + or - + or - Output Input + or - + or -

10. Positive Feedback Background sound + + Sound Ambient Sound + + + + Controller Controller Plant Plant + + Speaker Amplifier Previous Vibrations Sensor Sensor Guitar String w/ pickup Plucked String String Vibrations 2 possible models Vibrating Guitar String Amplifier Speaker Magnetic Pickup Positive Feedback Clip

11. Positive Feedback • Positive feedback is used to increase the actuation in the loop. • Advantages • Increased results • Faster results • Finds extremes • (maxima and minima) • Disadvantages • Consumes energy • Subject to local extremes (introns) • May become unstable • May destroy system • Examples: • Metal finders • Searches • Stock market programs • Genetic Algorithm performance measure build population test Worst Best Culled from Population create mutations Results

12. Negative Feedback Error Signal Disturbance + + + Controller Controller Plant Plant Output - Input Sensor Sensor Salt Desired Heart Beat + + + Heart Beat - Parasympathetic/Sympathetic System Heart homeostasis Nerves

13. Negative Feedback • Negative Feedback is used to reduce error • Advantages • Controls to a set point • Robustness to disturbances (uncertainty) • Rejection of distortion • Disadvantages • Prone to oscillation • Instability • Complexity • Coupling • Examples • Set point control • Tracking • Chang the system dynamics

14. Basic Control Actions • Bang – Bang • Most are on – off controls where either something is turned on or turned off in response to sensor: • If the error signal is greater than e1, turn system on • If error is signal is less than e2, turn system off • e1 and e2 are usually not be the same value • The control action could be reversed • Example: Sump pump • if water level is above 20, turn pump on • if water level is below 5, turn pump off

15. Basic Control Actions • Proportional • Control action is proportional to the error sensed • command = K * error signal • K is often called the “gain” of the controller • Example: Volume knob on the radio

16. Basic Control Actions • Integral control • control command is based on the size of the error and the length of time the error has existed • Example: Ripening of fruit • when fruit ripen they release ethylene • the ethylene increases the rate of ripening Ripening fruit

17. Basic Control Actions • Derivative control • control command is based on the magnitude and the rate of change of the error • Rarely alone used because of instabilities created by the speed of changes • Example: Pollution control of furnace

18. Basic Control Actions • Combined • PID (Proportional – Integral – Derivative) • sums all three actions • Most used control strategy • Example: Motor controllers

19. Summary • Open Loop • Closed Loop • Feedback • Positive feedback • Negative Feedback • Basic Control Actions • Bang-bang • Proportional • Integral • Deriviative • PID • Next: Modeling