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ENGI 128INTRODUCTION TO ENGINEERING SYSTEMSLecture 10:Feedback Control“Understand Your Technical World”11Mechatronics and Haptic Interfaces Lab
onics and Haptic Interfaces Lab
Disturbance Rejection: Artificial System3“Big Dog”, www.bostondynamics.com3Mechatronics and Haptic Interfaces Lab
Engineering Intelligent Systems4Roeder KD (1948) Organization of the ascending giant fibre system in the cockroach.4Mechatronics and Haptic Interfaces Lab
Disturbance Rejection: Natural System “Preflexes”(Recovery in 27ms!)5Jindrich, D. L. and Full, R. J. (2002). Dynamic stabilization of rapid hexapedal locomotion. Journal ofExperimental Biology. 205,2803-2823. (Video and picture courtesy Devin Jindrich)5Mechatronics and Haptic Interfaces Lab
Controlling Engineering SystemsOpen Loop vs. Closed LoopFeedback vs. Feedforward6Mechatronics and Haptic Interfaces Lab
Types of Control: open loopo Open Loop Control - sprinkler system7Mechatronics and Haptic Interfaces Lab
Types of Control: feedbacko Feedback control - Oven8Mechatronics and Haptic Interfaces Lab
Types of Control: feedback Winter growing up in Ohio9Mechatronics and Haptic Interfaces Lab
Types of Control: feedforwardo Feedforward control –the egg toss10Mechatronics and Haptic Interfaces Lab
Why use feedback control or better, why do you need a control system at all? consider ovens, A/C units, airplanes, manufacturing,pumping stations, etc What are we controlling? some physical quantity (constant) a dynamic behavior (a function of time) We need to 'tell' the system how we want it to behave11Mechatronics and Haptic Interfaces Lab
How do we ‘tell’ a system how to behave? turn a dial type a number But we need to know how well we are doing! sensor data (temperature, pressure, speed, position, light, etc)12Mechatronics and Haptic Interfaces Lab
OK, I know what I want the system to do. andI can monitor what the system is actuallydoing. Now what?13Mechatronics and Haptic Interfaces Lab
Control Ensure stability System maintains desiredoperating point (hold steadyspeed) Improve performanceActuateThrottle System responds rapidly tochanges (accelerate to 6 m/sec)SenseSpeedCompute Guarantee robustness System tolerates perturbations indynamics (mass, drag, etc)14Mechatronics and Haptic Interfaces Lab
Sample control systemsreferenceFeedforwardControllerreferenceor ‘set Mechatronics and Haptic Interfaces Lab
Feedforward putControl element responds to change in command ormeasured disturbance in a pre-defined wayBased on prediction of plant behavior (requires model)Can react before error actually occurs Overcome sluggish dynamics and delays Does not jeopardize stability16Mechatronics and Haptic Interfaces Lab
One implementation of feedforwardDesired outputInverse modelof systemInput neededfor desiredoutputPLANToutputModel-based prediction of inputIdeally consists of exact inverse model of the plantCan compensate for known plant dynamics, delays (beforeyou get errors)No sensors neededSystem response must be predictable17Mechatronics and Haptic Interfaces Lab
Limitations of feedforward controlEffects of disturbance or command input must bepredictableMay not generalize to other conditionsWill not be accurate if the system changes18Mechatronics and Haptic Interfaces Lab
ToutputSensorPlantReferenceControllerSensorSystem to be controlledDesired value of output (also ‘set point’)Computes compensatory command to theplant based on error(implied)19Mechatronics and Haptic Interfaces Lab
Features of Toutput Reactive / Error-driven Automatically compensates for disturbances(controller acts on error) Automatically follows change in desired state (setpoint can change) Can improve undesirable properties of system/plant Can be very simple20Mechatronics and Haptic Interfaces Lab
Combining feedback and feedforwardFeedforward and feedback are often used together Feedforward component provides rapid response Feedback component fills in the rest of the response accurately,compensating for errors in the FeedbackControllerinputoutputPLANT21Mechatronics and Haptic Interfaces Lab
Negative vs. Positive feedback22Mechatronics and Haptic Interfaces Lab
[whiteboard – PID control]23Mechatronics and Haptic Interfaces Lab
The Simplest feedback controller A proportional (P) controller In a proportional controller, the control action is proportional tothe error, and we can represent the controller as a gain, Kp. Represent with block diagram:24Mechatronics and Haptic Interfaces Lab
Limitations of P-control There are many times when you want the output of asystem to be equal to the input value. The proportional controller amplifies the error and applies acontrol effort to the system that is proportional to the error. P-controller must have some error in order to provide controloutput If you want better error performance, you might want toconsider using an integral controller In integral control, the control effort is proportional to the integralof the error So what?25Mechatronics and Haptic Interfaces Lab
Integration An integral is really the area under a curve. Let's assume that the independent variable is time, t. Then as time goes on the area accumulates. In math courses when they talk about integration, they picture it asthe limit of a process of taking small incremental areas - shownbelow - and letting the interval, T, shrink to zero. In digital integration, that visualization process is important.26Mechatronics and Haptic Interfaces Lab
Summary of Integrator behavior If output level matches the desired level, the error is 0 Because error is 0, the integrator output doesn’t change Because the integrator output doesn't change, if the restof the system is at steady state nothing else changes. This sounds too good to be true. What could possibly gowrong?27Mechatronics and Haptic Interfaces Lab
Integral control in a digital system Often implemented in code in some programminglanguage like C (or Python!). To implement integral control you use an approximationto the integral. The integral computation is updated by adding an areaequal to the latest measurement multiplied by thesampling period between measurements (the width ofthe rectangle).28Mechatronics and Haptic Interfaces Lab
Pseudo-code for integral controller ErrorInt 0/reset the integral approximation/MeasuredOutputn MeasureVolts(instrument) /Measure the output/Errorn DesiredOutput – MeasuredOutputn /Compute Error/ErrorIntn ErrorIntn-1 DT*(Errorn)/Integrate Error/VoltsOutn IntegralGain*ErrorIntn/Compute output voltage/OutputVoltage(VoltsOut)/Output the control signal/ This code assumes that you have a function MeasureVolts - that will measure voltage using aninstrument connected to the computer, and can output avoltage with a function - OutputVoltage - that usesanother instrument connected to the computer.29Mechatronics and Haptic Interfaces Lab
Performance, Stability, RobustnessImprove performanceEnsure robustness(e.g., response time of afirst order system)(e.g., minimize change in outputresponse for variations in input)Stabilize a response(e.g., reduce oscillatory effects)30Mechatronics and Haptic Interfaces Lab
Two main principles of feedbackRobustness to uncertainty through feedback Allows high performance in the presence of uncertainty Accurate sensing to compare actual to desired, correctionthrough computation and actuationDesign of dynamics through feedback Allows the dynamics (behavior) of the system to be modified Interconnection gives closed loop that modifies natural behavior Leverage capability to enhance performance or affect stability31Mechatronics and Haptic Interfaces Lab
Limitations of FeedbackReactionary solution that relies on existence andobservance of errorDisturbances applied to system will generate errorsResponse will be delayed (disturbance rejection)Trade-offs exist between performance and stabilityEffects of delay in the feedback path lead to instabilities32Mechatronics and Haptic Interfaces Lab
Summary of closed-loop feedback controlReactive controller based on error between desired andactual statesAutomatically compensates for external disturbances andfollows changes in commandSignificant impact on overall system responseUsed extensively in both natural and artificial systemsLimitations: Error must be present before actions taken Tradeoff between performance and stability33Mechatronics and Haptic Interfaces Lab
Integral control in a digital system Often implemented in code in some programming language like C (or Python!). To implement integral control you use an approximation to the integral. The integral computation is updated by adding an area equal to the latest measurement multip
