Cyber-Physical Systems Feedback Control

Transcription

1 Cyber-Physical Systems Feedback Control ICEN 553/453 Fall 2018 Prof. Dola Saha 1

2 Control System in Action Honeywell Thermostat, 1953 Chrysler cruise control, 1958 Feedback Systems: An Introduction for Scientists and Engineers 2

3 Closed Loop Control Noise Disturbing forces Actuators U(t) Control commands Driving forces D(t) Desired state variables X*(t) Plant Real state variables X(t) State estimator Sensor outputs Sensors Y(t) Analog Interface Noise Control Software Errors Compare X (t) Software ADC or input compare E(t)=X*(t)-X(t) Estimated state variables 3

4 Open Loop Control Ø Control Action is independent of the output of the system Desired state variables X*(t) Control commands Noise Driving forces Disturbing forces Controller Actuators Plant Real state variables U(t) D(t) X(t) 4

5 Open Loop Control Ø state estimator eliminated not well suited for a complex plant Ø assumes disturbing forces have little effect on the plant Ø less expensive than closed-loop control example: electric toaster 5

6 Example Problem: Bike in straight Line ØSteer the bike in a straight line blindfolded ØOpen loop à no sensor feedback ØWhat if you hit a rock? ØWhat if the handle bars aren t perpendicular to the wheels? 6

7 Control Systems Strategy Ø Strategy plant is a system that is intended to be controlled collect information concerning the plant data acquisition system (DAS) compare with desired performance generate outputs to bring plant closer to desired performance Ø You can t control what you can t measure 7

8 Control Systems Ø Microcomputers are widely employed in control systems: automotive ABS, ignition and fuel systems household appliances smart things industrial robots pacemakers Ø Why are we interested in Feedback Systems in CPS course? 8

9 Control Systems Closed loop Ø Closed-loop control feedback loop implementation o suitable for complex plant sensors and state estimator produce representation/estimation of state variables these values are compared to desired values control software generates control commands based upon the differences between estimated and desired values 9

10 Closed Loop Control Ø Control action depends on the output of the system Desired state variables X*(t) Control commands Noise Driving forces Disturbing forces Controller Actuators Plant Real state variables U(t) D(t) X(t) Sensors 10

11 Example Problem: Bike in straight Line ØIf you can see the pavement à Closed Loop Approach ØControl based on error: PID ØProportional : Change handle angle proportional to the current error ØDerivative : Large handle corrections when error is changing slowly, and small handle corrections when error is changing quickly ØIntegral : Handle corrections based on the cumulative error 11

12 Problem: Set Motor Ø Open Loop Controller Use trial and error to create relationship between velocity and voltage Problems o Supply voltage change o Bumps in carpet o Motor Transients Desired To Volts Motor Actual 12

13 Problem: Set Motor Ø Closed Loop Controller Feedback is used so that the actual velocity equals the desired velocity Can use an optical encoder to measure actual velocity Desired err Controller Adjusted Voltage Motor Actual 13

14 Step Response with No Controller Desired To Volts Motor Actual Ø Naive velocity to volts Ø Model motor with several differential equations Ø Slow rise time Ø Stead-state offset Time (sec) 14

15 Step Response with Proportional Controller Desired Controller (V des ) err Adjusted Volts (X) des Ø Big error big = big adj Ø Faster rise time Ø Overshoot P ( V V ) X = V + K - des Ø Stead-state offset (there is still an error but it is not changing!) act Motor Actual (V act ) Time (sec) 15

16 Step Response with PD Controller Desired Controller (V des ) err Adjusted Volts (X) X = V des + K e( t) - Ø When approaching desired velocity quickly, de/dt term counteracts proportional term slowing adjustment Ø Faster rise time Ø Reduces overshoot P K D de( t) dt Motor Actual (V act ) Time (sec) 16

17 Step Response with PI Controller Desired Controller (V des ) err Adjusted Volts (X) X = V + K e( t) - K e( t dt des P I ) Ø Integral term eliminates accumulated error Ø Increases overshoot ò Motor Actual (V act ) Time (sec) 17

18 Step Response with PID Controller Desired Controller (V des ) err Adjusted Volts (X) Motor Actual (V act ) Ø Combined benefits of PI and PD X = V des + K - K I D + K ò P e( t) dt de( t) dt e( t) Time (sec) 18

19 Control Systems Performance Ø Performance metrics steady-state controller error o an average value of the difference between desired and actual performance transient response o how quickly the system responds to change stability o system output changes smoothly without oscillation or unlimited excursions 19

20 General Approach to PID U( t) Ø Proportional Ø Integral Ø Derivative Ø PID t = K E( t) + ò K E( t ) dt + p 0 i U p = K p E K de( t) dt U i = U i + K i E t U d = K d (E(n)-E(n-1))/ t U = U p + U i + U d d 20

21 PID Performance Measure Ø Accuracy Magnitude of the Error = Desired Actual Ø Stability No oscillations Ø Overshoot (underdamped, overdamped) Ringing, slow Ø Response Time to new steady state after Change in desired setpoint Change in load underdamped t response 21

22 Comparison Controller Response time Overshoot Error Open-Loop Smallest Highest Large Proportional Small Large Small Integral Decreases Increases Zero Derivative Increases Decreases Small change 22

23 Parameter Tuning Ø Manual Tuning Ø Ziegler Nichols Tuning Time Domain Method Frequency Domain Method Ø Relay Feedback Ø Integrator Windup 23

24 PID Controller in Software Ø Wait for clock interrupt Ø Read input from sensor Ø Compute control signal Ø Send output to the actuator Ø Update controller variables Ø Repeat 24

25 PID Controller Pseudocode 25

26 Proportional Controller to Helicopter Problem desired angular velocity error signal net torque 26

27 Controller Summary Ø Controller only as good as its sensor Ø Observe everything What was it thinking? Ø Change one parameter at a time Ø Choose stability over responsiveness 27