ca4 slides

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?