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MAXX WILSON | MELISSA CRUZ

MAY 2022

Final Presentation

ME397 Real-Time Control Systems Lab

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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Introduction and Objectives

Automotive suspension systems utilize active suspension to maximize passenger comfort.

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Objective:

Reduce Body Acceleration

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Elattar, Yahia & Metwalli, Sayed & Rabie, Mahmoud. (2016). PDF VERSUS PID CONTROLLER FOR ACTIVE VEHICLE SUSPENSION.

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Introduction and Objectives

Many models can be simplified into an inverted pendulum: rocket ships, humanoids

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Objective:

Regulate pendulum to vertical and specify hub setpoint

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Schperberg, Alexander & Shirai, Yuki & Tanaka, Yusuke. (2019). Reducing Motion Perturbation for a Bipedal Robot using Model Predictive Control. 10.13140/RG.2.2.27143.55207.

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Project Objectives

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Demonstrate state estimation and various control methodologies for the Active Suspension and Inverted Pendulum, in real-time.

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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System Modeling - Active Suspension

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System Modeling - Inverted Pendulum

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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Data Acquisition

Active Suspension

  • National Instruments Compact RIO
  • Samples at 500 Hz
  • 16-bit ADC (depending on cRIO model)
  • Accelerometer and Encoders

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Inverted Pendulum

  • National Instruments myRIO
  • Samples at 100 Hz
  • 12-bit ADC
  • Two Encoders

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

  • Design
  • Validation

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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Filters - Active Suspension

Objective:

  • Remove noise while capturing system dynamics

Observations:

  • Nyquist frequency (~1500 rad/s) exceeds bandwidth of body velocity (~70 rad/s)
  • Velocity estimate from acceleration is always attenuated by integrator

Outcome:

  • Place initial cutoff frequencies at bandwidth frequency

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Filters - Inverted Pendulum

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Observation:

  • No 3dB cutoff frequency for hub and pendulum velocity

Outcome:

  • Initial filters set to Nyquist frequency (50Hz or 314 rad/s)

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

  • Design
  • Validation

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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Filters - Active Suspension

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Filters - Active Suspension

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Filters - Inverted Pendulum

Observation:

  • Experimentation saw error at small amplitudes from ADC resolution

Outcome:

  • Moved cutoff to 50 rad/s and damping of 0.707.

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Filters - Inverted Pendulum

Observation:

  • Experimentation saw error at small amplitudes from ADC resolution

Outcome:

  • Moved cutoff to 50 rad/s and damping of 0.707.

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

  • Design
  • Validation

Linear Controllers

Advanced Controllers

Summary and Future Work

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Active Suspension Kalman Filter

Estimation of sensor variance:

  • Estimated encoder variance to be 1/100th mm by recording measurement resolution
  • In practice, bias will contribute more to encoder inaccuracies than resolution/noise (which are very small)
  • Set encoder variance to 3mm to match default resolution of Labview script
  • Estimated accelerometer variance using average sensor noise of system at rest
  • Final R Matrix values: 3 mm for encoder, 0.0017 m^2/s^4 for accelerometer

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Encoder Resolution

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Inverted Pendulum Linear Observer

Given state space model of system, check observability in Matlab

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For initial guess, set Observer poles around 10x faster than system poles and solve for gains

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System Poles

Observer Poles

Observer Gains

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

  • Design
  • Validation

Linear Controllers

Advanced Controllers

Summary and Future Work

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Active Suspension Kalman Filter

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Tire Position/Velocity

Vehicle Body Position/Velocity

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Active Suspension Kalman Filter

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Kalman Filtering Results:

  • Tuning and validating was very difficult
  • Assumption of linear dynamics degrades performance (motivates Extended or Unscented Kalman Filter)
  • Unmodeled dynamics/disturbances are problematic
  • May be beneficial to use accelerometer to estimate road velocity disturbance
  • Without estimation of disturbance, model performs worse in transients and lags true state

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Inverted Pendulum Linear Observer

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Experimental Adjustments:

  • Removed imaginary component to reduce oscillation
  • Pushed poles farther left to increase tracking performance

Outcomes:

  • Good position tracking, high gain velocity tracking resulted in oscillation

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

  • Design
  • Validation / Discussion

Advanced Controllers

Summary and Future Work

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Active Suspension LQR Design

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Determine initial Q and R using Bryson’s Rule

Initial maximum allowable force magnitude, ui : 25 N

Half of the saturation limit in Labview

Initial max acceptable value of states, xi: determined by system response to 1 cm disturbance

Uncontrolled body velocity (blue) and tire velocity (red) for periodic 1cm disturbance

Uncontrolled body acceleration for periodic 1cm disturbance

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Active Suspension LQR Design

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Included 2nd order low pass filter from Lab 3 to decrease system oscillations from noise

Final “Bryson’s Rule” Weights

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Inverted Pendulum Pole Placement

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Initial controller poles placed on left hand side

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K =�-0.0023�1.6532�-0.5518�0.0317

Used 2nd order low pass filter from Lab 3 to reduce oscillations from noise

2nd order low pass filter performance

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

  • Design
  • Validation / Discussion

Advanced Controllers

Summary and Future Work

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Inverted Pendulum Pole Placement

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Simulated Response Experimental Response

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Hub response for 20° Periodic reference, Pendulum response for 0° reference

Experimentally Determined Poles:

p1 = -7; p2 = -70; p3 = -6; p4 = -5;

K = -3.39, 21.71, -2.36, 2.89

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Active Suspension LQR Results

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Simulation Results:

Controlled body velocity (blue) and tire velocity (red) for periodic 1cm disturbance

Uncontrolled body acceleration for periodic 1cm disturbance

Experimental Results for 1 cm periodic disturbance:

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Active Suspension LQR Results

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Experimental Results for 1 cm periodic disturbance (cont.):

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

  • Design
  • Simulation
  • Validation / Discussion

Summary and Future Work

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Model Predictive Control - Formulation

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Model Predictive Controller Attributes:

  • Unconstrained Quadratic Programing problem
  • Quadratic cost function
  • Control inputs as sole optimization variables allows for longer prediction horizon
  • “Shooting Method”

Experiment Steps:

  • Convert algorithm for system matrices into code
  • Normalize weights by horizon to decouple them for tuning
  • Measure execution speed to estimate acceptable horizons

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

  • Design
  • Simulation
  • Validation / Discussion

Summary and Future Work

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Model Predictive Control - Active Suspension

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Simulation:

  • Started at default weights, as MPC tuning is intuitive and simulation is safe/quick
  • Decreased position weight
  • Increased body velocity weight
  • Added small weight to tire velocity to dampen high frequency oscillations
  • Increased effort weight to limit within saturation

Final Parameters:

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Natural Response, f=0.3Hz, A=0.01m

Forced Response, f=0.3Hz, A=0.01m

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Model Predictive Control - Inverted Pendulum

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Initial Parameters:

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Caused excessively large control inputs

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Final Parameters:

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Decreased hub angle weight

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Added small hub velocity weight for damping

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Increased control input weight to fit within saturation

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

  • Design
  • Simulation
  • Validation / Discussion

Summary and Future Work

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Model Predictive Control - Active Suspension

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Reducing passenger acceleration is the priority!

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Model Predictive Control - Active Suspension

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Model Predictive Control - Inverted Pendulum

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Presentation Roadmap

Introduction and Objectives

System Modeling

Data Acquisition

Filters

Estimators

Linear Controllers

Advanced Controllers

Summary and Future Work

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Summary and Future Work

To conclude, using the Active Suspension and Inverted Pendulum we’ve shown:

  • 1st and 2nd Order Low Pass Filters
  • Linear Observer and Kalman Filter Estimators
  • Linear Control through Pole Placement and LQR
  • Advanced Control using Model Predictive Control
  • Simulation and Experimental Validation

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Summary and Future Work

Notable areas of future work include:

  • Improved state estimation models
    • Linearization of full non-linear models
    • Estimation of previously unmodeled and untracked disturbances
  • Improving smoothness in pendulum MPC
    • Add jerk component to cost function
    • Increase control horiz
  • Add constraints and initial guess to MPC
  • Run MPC at lower frequency and buffer/interpolate control inputs

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Questions?

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