1Title slide

sstamatov@dspaceinc.com

(248) 303-0944

University of Detroit Mercy

Modeling and Control of Quarter Vehicle Modeling and Control of Quarter Vehicle Suspension with a Semiactive ActuatorSuspension with a Semiactive Actuator

Dissertation Defense PresentationDissertation Defense Presentation

Stamat Stamatov

12/3/2008

Advisors: Dr. Mohan Krishnan Dr. Sandra Yost

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The Beginning

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Introduction to Semiactive Suspensions

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HondaCopyright Hitachi

Semiactive suspension components

Hitachi Semiactive suspension components

(height sensor not shown)

Audi front suspension

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Semiactive Damper Design 1

(copyright Xubin Song)

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Semiactive Damper principle of operation

(copyright Carbibles.com)

Semiactive Damper Design 2

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Semiactive Suspension Control System Structure

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Semiactive Suspension Modeling

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Double Wishbone Quarter Vehicle Suspension Modeling

Realistic drawing 2D model mechanical diagram

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Quarter Vehicle Suspension Model Decomposition

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Body and Wheel Model 1

Challenges:

• Body, wheel, lower & upper arm form a kinematic loop (many constraint equations and only two degrees of freedom: Yb, Yw)

• The equations of motion are highly nonlinear due to the trigonometry involved.

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Body and Wheel Model 2

Solution:

• Manually solve and optimize the equations of motion (used symbolic algebra package).

• For simplicity represent the equations of motion as a second order differential equation with varying coefficients (PXX).The coefficients are functions of the current system states (body to wheel distance).

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Body and Wheel Model 3

Nonlinear coefficient loop is shown in grey

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Strut Model 1

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Strut Model 2

Challenge:

The magneto rheological damper is highly nonlinear and exhibits hysteresis

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Bouc-Wen hysteresis model used for the MR damper

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MR damper Bouc-Wen hysteresis model– Simulink Diagram

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Tire model

The tire is a slightly nonlinear spring (with slight damping).

Tire hop needs to be taken into account.

The camber force needs to be taken into account FC = f(FN,γC)

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Tire model – Simulink diagram

Tire hop and nonlinear stiffness are taken into account.

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Simulink model Real time model considerations

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Workflow: Symbolic Math Formulae ► Simulink Stateflow Model

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Entire quarter vehicle model - Simulink diagram

For this section see author's SAE article “Using Quasi-linearization for Real Time Dynamic Simulation of a Quarter Vehicle Suspension” 2007-01-0833

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Pre-calculating complex expressions into lookup tables

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Different Integration Methods for Different Feedback Loops

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Speedup of model when lookup tables are used

Model Execution Time

0 1 2 3 4 5 6 7 8 9 10

Coeff from

formulae, cont.

time

Coeff from

formulae, discr.

time

Coeff from

Lookup tables

execution time in microseconds

Execution times of models on a dSPACE DS1006 board with 2.2 GHz Opteron processor.

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Optimizing the Simulink model for speed

• Pre-calculate into lookup tables the nonlinear PXX coefficients of the Body & Wheel equations

• Pre-calculate into lookup tables the transformation from body to wheel distance into suspension angles.

• Use different rates for different parts of the model (faster rates only for stiff or low time constant loops).

• Use different integration methods depending on the feedback loop location. (Euler Forward where there is immediate feedback to from integrator output to input).

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Ride Comfort Criteria

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Passenger comfort criteria

• AccelerationVehicle body vertical acceleration is considered the main criterion for passenger comfort. RMS acceleration value is most commonly used.

JerkJerk (the derivative of vehicle body acceleration) is taken as the second most important passenger criterion.Peak jerk, filtered peak jerk, and RMS jerk are to be used (in that order of importance)

• Acceleration PSD To account for frequency – acceleration power spectral density (PSD) function is used.

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On the Importance of Jerk as Passenger Comfort Criterion

• Improperly designed semiactive control algorithms can introduce significantly higher jerk levels than passive suspensions.Abruptly changing control forces (due to a nonlinear control algorithm or a nonlinear actuator) contribute to abrupt changes in vehicle body acceleration and thus to higher jerk levels.

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Semiactive Control of Quarter Vehicle Suspension

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Linear Two-Mass Model

A simple linear two-mass model is used for controller design.

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State Space Linear Model 2

A state space model representation better suited for control with the available measurements (YBW).

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Semiactive Dampers as Actuators Limited Working RegionRisks of higher Jerk Levels

34A semiactive damper can deliver the requested forceonly part of the time

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Limited Working Region of Semiactive Damper 2

As the damper working region is exited, the force with the sign requested by the control algorithm can no longer be delivered and the current is shut off.

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Force jumps with abrupt on/off switching of the damper - 1

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Force jumps plot - 2

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Jerk Mitigation

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Basic Idea Behind Jerk Mitigation

• Force requests need to be modified when near the borders of the damper working region.Gradually lower damper force (damper current) before damper reversal.Gradually increase damper force (damper current) after damper reversal.

• Avoid abrupt force reversal requests from the control algorithm.If such request is issued - limit slew rate of the force request.

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Jerk Mitigation – Desired Behavior

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Jerk Mitigation – Desired Behavior 2

The goal is to modify (modulate) the force request:

- Only when close to the border of the damper working region.

- Only a short time before exiting and short time after re-entering the damper working region.

- The goal is to avoid fast rate of change of the force request. Thus lowering of force should start early enough before the moment force should reach zero.

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Jerk Mitigation Modulation – Block Diagram

The output of the control algorithm is modulated to achieve smooth transitions.

Patented by Virginia Tech. with the smoothing function - a static surface.

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Jerk Mitigation Static Surface modulation

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Jerk Mitigation Static Surface modulation

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Jerk Mitigation Static Surface modulation – example 2

Smoothing function surface patented by Mehdi Ahmadian, Xubin Song

Alternative smoothing function surface suggested by the author

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Static Surface modulation – Modulated Current Graph

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The tuning of static surface (level) based modulation is a compromise between low and high speed behavior.

Level (surface based) Modulation at Various Damper Speeds

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The tuning of static surface (level) based modulation is a compromise between low and high speed behavior.

Level (surface based) Modulation at Various Damper Speeds

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Prediction based Jerk Mitigation Modulation

C(t) is a function indicating entering/exiting damper working region.

Predict when C(t) will cross zero and modulate damper force in advance.

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Jerk Mitigation Modulation – Using Zero Crossing Predictor

C(t) is a function indicating entering/exiting damper working region.

Predict when C(t) will cross zero and modulate damper force in advance.

See the author's SAE article “Low Jerk Predictive Force Modulation for Semi-Active Suspension Control” 2008-01-0904

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Modulation coefficient with Zero Crossing Predictor - 2

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Comparison of modulation approaches

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Control Command

(Damper Current)

Real Time Demo

Plant Model

Controller Algorithm

Sensor Measurements

Load models

as C code

Monitor Simulation

400Hz CAN

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Summary of what may be considered new in this work

Easy to analyze 2D quarter vehicle suspension Model presented as simple equation with varying coefficients.

Model optimized for real time execution.

Workflow/Process to derive, simplify models and create real time capable implementations.

Approach to filtering of PSD functions for easier comparison.

Comprehensive treatment of Jerk mitigation requirements and approaches.

New dynamic algorithm for jerk mitigation. The algorithm would use a predictor to anticipate the moment when the damper will no longer be able to deliver the required force.

Study of optimal tuning of skyhook-groundhook controller and its effects on jerk.

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Papers written as part of this research

“Using Quasi-linearization for Real Time Dynamic Simulation of a Quarter Vehicle Suspension” 2007-01-0833with co-authors Dr. Sandra Yost and Dr. Mohan Krishnan

The paper was selected for the SAE’s 2007 Transactions

“Low Jerk Predictive Force Modulation for Semi-Active Suspension Control” 2008-01-0904

with co-authors Dr. Sandra Yost and Dr. Mohan Krishnan

The paper was presented at the SAE’s 2008 World Congress.

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The End