Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Lecture 12 This week: • Lab 20: Internal Model Control (session 2) • No lab on wed/thurs – Happy Thanksgiving Week of 12/2: • Lab 22: Integrative Lab – Electrohydraulic Force/Torque Control (2 to 3 sessions) • Review lecture: 12/6 Final Exam on 12/17 (Tuesday): 10:30am-12:30 Today’s lecture: • Review of various control algorithms M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Your Feedback on E-H Control Labs so far Interesting helpful • Doing control experiments on real systems • PID control • Correlating actual response to theory and simulations • Matlab / SIMULINK • Clean – not covered in oil!
Confusing • • • • • •
Physical setup Too much writing Too many steps Pre-labs to require analysis Big picture Inconsistency between lab procedures and report requirements (mainly lab 18) • SIMULINK/System concepts
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Electrohydraulic Force/Torque Control
Objective: • Accurately apply predefined force/torque (stress) trajectories to specimen • Often until fails
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Setup and Procedures • Linear system: Actuator pushing against a leaf spring (one end constraint). Force measurement by load cell. • Rotary system: Actuator torquing an aluminum rod. Torque measurement by torque cell. • It is a new system ! • Expect some nonlinearity of the spring • Apply all your knowledge !
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Objectives: Design and implement controllers to accurately track different types of trajectories Steps: 1. System identification (valve command input, force/torque output) 2. Choose appropriate controllers for the trajectories (steps, biased sinusoids, triangular wave) 3. Analyze and design controllers 4. Implement control 5. Go to steps 2/3 and improve performance
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Critical Basic Concepts • Transfer function • Input-output relationship • Block diagram à transfer function • Closed loop pole locations and characteristics of response • Stability • Steady state response via final value theorem • Frequency response
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Critical Controls Concepts Control system objectives: • Stability: Determined by closed loop pole location • (Reference Tracking) Performance: • Robustness to disturbance • Insensitivity to model uncertainty • Immunity to measurement noise
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Feedback versus feedforward • Feedback control • Advantages: Compensates for disturbances and model uncertainty • Disadvantages: • Can be unstable if not designed correctly • Usually cannot track ARBITRARY reference trajectories PEFECTLY • Feedforward control • Advantages: Perfect tracking for ARBITRARY reference trajectories! • Disadvantages: Cannot compensate for disturbances or model uncertainty • Feedback and feedforward control can be combined!!!! • TRY it for your lab 22! • Feedforward keeps error small so that higher feedback gains can can be possible M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
Comparison of Feedback Controllers Proportional Control • Advantage: • Simple • Disadvantages: • Need infinity gain to good performance, • Increases gain in all frequencies • Compromise with noise and robustness, • Steady error with constant disturbances or ramp (and step in general) inputs
M..E., University of Minnesota (updated 12.2010)
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Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Proportional-Integral Control Advantages: • Zero-steady state error for step (and ramps in general) references and disturbances • Increases low frequency gain while keeping high frequency gain low • Steady state error relatively insensitive to model uncertainty Disadvantages: • Works only for limited set of reference trajectories and disturbances • 2 gains to tune • 2nd order closed loop system (with 1st order plant) à possibility of resonance, under-damped etc.
Good for situations when required control input (in steady state) is a constant M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Internal Model Control (Generalized P-I) • Advantage: • Zero-steady state error for step, ramps, sinusoids, exponential etc. references and disturbances • Increases gain at the specific frequency of references while keeping gains at other frequencies low • Insensitive to model uncertainty as long as closed loop is stable • Disadvantage: • Works only for limited types of reference trajectories and disturbances • Many gains to tune • Complex – needs to relies on analysis
M..E., University of Minnesota (updated 12.2010)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)
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Control Design Procedures 1. What is the system being controlled? • Model it • System identification 2. Choose the type of controller • P, PI, IMC, Feedforward etc.) 3. Formulate closed loop transfer function, and analyze performance 4. Design desired pole locations (where should they be?) 5. Calculate the controller gains to obtain the poles 6. Add feedforward control M..E., University of Minnesota (updated 12.2010)
