ca4 slides
DESCRIPTION
CA4 Slides CA4 Slides CA4 SlidesTRANSCRIPT
Project Scope - ITreating the Dual-Stage Actuator as 2
individual Single-Stage ActuatorsOne Actuator operating at any one timePrimary: VCM Actuator (PZT off)Secondary: PZT Micro-actuator (VCM off)Dual-Stage: Power up VCM + PZT
Project Scope - IIFor each actuator, perform: - Frequency Response Measurement - System Identification, G(s) - Notch Filter Design, F(s) - Controller Design, C(s) - Discretization, C(z)F(z) - Hardware Controller Implementation
Then design for Dual-Stage Actuator - Master-Slave Decoupling/PQ Method etc.
What has been done IVCM Frequency Response Measurement System Identification Notch Filter Design Controller DesignDiscretization Hardware Controller Implementation
What has been done IIPZT micro-actuatorFrequency Response MeasurementSystem Identification Notch Filter DesignController DesignDiscretization
What has been done IIIMain focus: VCM - Explore - Simulate with different controllers - Compare simulation results with
experiment - AnalyzePZT simulations - Could be used by interested learners for
hardware test
System Identification IVCM Experimental Frequency Response vs.
Identified VCM Model
Model:
System Identification IIRigid body model - Repeated pole at around 1 kHzResonant Modes - in-phase mode = 2 poles - out-of-phase mode = 2 zeroesExtraction of Modal Parameters - natural frequency = frequency at resonant peak - small damping ratio - (half-power bandwidth) damping ratio ≈ (ωa-ωb)/2ωr
System Identification IIIResonant Modes, i Resonant
Frequency (kHz)Damping Ratio, ζi
1 4.29 0.0043 2 7.29 0.0051 3 7.86 0.0062 4 9.63 0.0204Anti-resonant Modes, j
Anti-resonant frequency (kHz)
Damping Ratio, ζi
1 4.43 0.0044 2 7.61 0.0087 3 8.92 0.0068
Modal Parameters of the identified VCM model
Notch Compensation4 Notch Filters Designed for the 4 resonant
modes above7 Notch Filters used initiallyNotch Filters brings about drastic phase changesLeads to implementation problem on DSP
Desired Frequency Domain for Controller Design
- Closed-loop Stability: 6 dB GM, 40 deg PM- Disturbance Rejection: High gain at low frequency range- Low High frequency Gain: Reduce noise amplification
PI-Lead Controller Design Integral Control with Lead CompensatorIntegrator: Infinite gain at low frequencyLead: Boosts PM at gain c/o frequency
Lag-Lead Controller Design ILag: Increases low frequency gainReduced steady state errorLag-Lead chosen over PI-Lead: unidentified problem with DSP during PI implementation
Closed-loop Step Response I
Discretization and SimulinkSource:unit square wave input40 kHz sampling frequencyTustin approximation
Hardware Implementation of the Lag-Lead Compensator IUndue vibration observed from the VCM plantIndication of InstabilityLarge oscillations
Problem Identification and Controller RedesignMismatch between VCM bode plot and the
plot of the identified model (slide 6)Gain lowered at low frequencies (slide 7)Pure gain added for adjustment (slide 8)Resonant modes are the sameLag-Lead Compensator Redesigned
Problem Identification contd.
Problem Identification contd.
Controller Redesign II (gain c/o frequency = 460 Hz)
Closed-loop Step Response II
Hardware Implementation of Lag-Lead Compensator II (gain c/o = 460 Hz)Small BandwidthSlow ResponseOscillationsBandwidth can be increased
Controller Design III (gain c/o frequency = 955 Hz)
Closed Loop Step Response III
Simulink Plots for Discrete-time ISource: Unit Square Wave Input40 kHz Sampling frequencyZOH method
Simulink Plots for Discrete-time IISource: Saw-tooth wave40 kHz Sampling frequencyTustin method
Simulink Plots for Discrete-time IIISource: Sine Wave40 kHz Sampling FrequencyTustin method
Hardware Implementation of Lag-Lead Compensator III (gain c/o = 955 Hz)Faster responseIncreased oscillationsPossible drawback in notch designVariation in VCM resonant modesWider notch filter could be used
Control Design ResultsOpen-loop transfer function
GainMargin(dB)
PhaseMargin(deg)
Gain c/oFrequency(Hz)
Overshoot(%)
Rise time(s)
Settling time (s)
Pvcm(s)Nvcm
(s)Cvcm(s)(460 Hz)
6.18 52.9 460 22.8 0.000181
0.00174
Pvcm(s)Nv
cm
(s)Cvcm(s)(955 Hz)
6.79 46.8 955 23.2 0.000186
0.00168
DesiredSpecifications
> 6 > 30 ˜1000 < 20 < 0.0002
< 0.002
PZT Micro-actuator: System Identification
PZT control: Lag Compensator cascaded with 4 Notch Filters
Closed-loop Step Response
Control Design ResultsGM = 13.3 dBPM = 49.2 degOvershoot = 12.8 %Settling time = 1.66 ms
Discretization and SimulinkSquare wave input source40 kHz Sampling frequencyTustin method
Questions?