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

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

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? 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 + Actuate Bench rest Bench 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 SensingComputeActuate

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

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

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: M etal finders Searches Stock market programs Genetic Algorithm build population create mutations test performance measure Results Culled from Population BestWorst

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

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 e 1, turn system on If error is signal is less than e 2, turn system off e 1 and e 2 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