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Model Predictive Control for Embedded Applications Leonidas G. Bleris Panagiotis Vouzis, Mark Arnold, and Mayuresh V. Kothare 2006 AIChE Annual Meeting San Francisco, CA. Introduction. Model Predictive Control Theory MPC for Portable Devices Implementation Pathways Applications

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Model Predictive Control for Embedded Applications

Leonidas G. Bleris

Panagiotis Vouzis, Mark Arnold, and Mayuresh V. Kothare

2006 AIChEAnnual MeetingSan Francisco, CA


Introduction
Introduction

  • Model Predictive Control

    • Theory

  • MPC for Portable Devices

    • Implementation Pathways

    • Applications

  • Concluding Remarks


Briefly
…briefly

A class of control algorithms that utilize an explicit process model

to compute a manipulated variable profile that will optimize an open-loop

performance objective over a future time interval.

The performance objective typically penalizes predicted future errors and

manipulated variable movement subject to constraints


History briefly
History (...briefly)

  • LQR (Kalman, 1964)

    • Unconstrained infinite horizon

  • Constrained finite horizon – MPC (Richalet et al., 1978, Cutler & Ramaker,1979)

    • Driven by demands in industry

    • Defined MPC paradigm

  • Posed as quadratic program (QP) (Cutler et al. 1983)

    • Constraints appear explicitly

  • Academic research: 919 papers in 2002... (Allgöwer, 2004)

    • Stability

    • Performance

  • Explicit MPC (Bemporad et al. 2002, Tøndel et al. 2003)

(Qin & Badgwell, 2003)


In detail
…in detail

Disturbances

Parameters

MPC

Umpc

System

Output

Uinitial

State-space

Transfer function

Step response

Impulse response

Model:

Predicted

outputs

Inputs

+

Reference

Model

-

Updated

Inputs

Optimization

Cost Function

+ Control & Prediction horizons + Weighting matrices

Constraints


Receding horizon solution
Receding horizon solution

Model

Optimization

Disturbances

Parameters

Umpc

System

Output

Uinitial

Set-point

Past

Future

Projected

output

Manipulated input

k

K+1

K+2

K+3

K+m-1

Prediction

Horizon

Control

Horizon



Constraints
Constraints

  • The three basic types of constraint; hard, soft and setpoint approximation.

  • Hard constraints (top) should not be violated in the future.

  • Soft constraints (middle) may be violated in the future, but the violation is penalized in the objective function.

  • Setpoint approximation of constraint (bottom) penalizes deviations above and below the constraint. Shades areas show violations penalized in the dynamic optimization.

Froisy, 1994


Output and input trajectories
Output and Input Trajectories

  • Four options for specifying desired controlled variables behavior:

    • setpoint

    • zone

    • reference trajectory

    • funnel.

  • Shaded areas show violations penalized in the dynamic optimization


Why mpc
Why MPC?

  • Ability to enforce constraints on manipulated and controlled variables

    • Economic operating point of typical processes often close to constraints…

  • Ability to handle large multivariable systems

  • Novel formulations (such as hybrid MPC) enable the application to systems involving both discrete-event and continuous variables.

    ..not

  • Problems with model uncertainties and over-parameterized models

  • MPC requires on-line optimization of a possibly large problem, at each control decision.

    • Using Newton’s algorithm, the number of operations is 12(n3+6n2+10n), where n is the size of the problem: (inputs) x (control horizon M)

Choosing an MPC technology for a given application can

be a complex task!


Why embedded mpc
Why Embedded MPC?

Need for advanced embedded controllers is inherent in multiple

application areas:

  • Biomedical / Prosthetics

  • Robotics

  • Automotive / Avionics

  • etc

    Desirable characteristics of an MPC chip?

  • Reliable operation

  • Low-power consumption

    • Small area

    • Small memory-size requirements

    • Operation in low frequency and voltage

  • Reconfigurability


Biomedical applications
Biomedical Applications

R. Dorf and R. Bishop, Modern Control Systems, Addison Wesley, 7th edition, 1995.


Drug delivery prosthetics
Drug Delivery - Prosthetics

  • American Diabetes Association: Industry size $11 billion

  • Nearly 6% of the U.S. population

Figure: Diabetes patients in US

  • “Smart” Prosthetics: Controllers for artificial limbs

  • Global market for neuromodulation, stimulation and neurosensors at US$2.4 billion for 2004 with expected annual growth of 32%

  • Neuronal prosthetics market, at US$2.2 billion by 2008

  • Need for MPC arises from the multivariable and constraint nature

    • Controller allows for flexibility and usability

    • Improves comfort and mobility of patients


Automotive
Automotive

Economist, September 2006



Mpc for portable systems
MPC for Portable Systems

NSF workshops:

  • The importance of control and system integration of microscale

    systems emphasized

  • “For self-contained miniaturized systems, the sensors, actuators and

    control hardware must be included within the system design.”

    One of the issues raised was that software and DSP based control:

  • may not be practical since they may take up too much “real estate” on the chip

  • might not be sufficiently fast for microscale system dynamics.

Shapiro B. Workshop on Control and System Integration of Micro- and Nano-Scale Systems, Technical Report, National Science Foundation Workshop, 2004

Sitti M. Workshop on Future Directions in Nano-Scale Systems, Dynamics and Control, Technical report, National Science Foundation Workshop, 2003


Implementation pathways
Implementation Pathways

  • S/W-H/W Co-Designed Embedded Controller

    • Customize the implementation according to the optimization algorithm and design/performance objectives

  • Application-Specific Processor

    • Speed and reduction in “real estate”

  • Off-the-shelf General Purpose Processor

    • No need for H/W design

    • Easy implementation since only programming is required

    • Unable to tailor the H/W to the particular needs of the problem


S w h w co design approach
S/W-H/W Co-Design Approach

Input (16 bits)

16-bit

µP

Core

Matrix

Coprocessor

+

LNS

Output (16 bits)

Write

Read

CS

Data or Status


Mpc formulation
MPC formulation

  • The optimization problem:

  • State-Space model of a system

  • Results to:


Computational issues in mpc
Computational Issues in MPC

P:Prediction Horizon

M:Control Horizon

N: Number of states

B = P×M

A = P×N

Yref = 1×M

  • Using Newton's method:

  • We get:

    where:

  • Abundant matrix operations


Hw sw partitioning
HW-SW Partitioning

Gradient, Hessian, Gauss-Jordan

Matrix Coprocessor

Newton, Initialization

ADCUS

  • µP used: ADCUS SE1608 16 bit

  • FPGA used: Virtex IV of Xilinx

  • Development environment: ISE 7.1 of Xilinx & EISC Studio of ADCUS

Profiling results for a benchmark control

problem on a Pentium processor.


Profiling and timing results of the adcus coprocessor architecture
Profiling and Timing Results of the ADCUS-Coprocessor Architecture

The clock cycles required by each function of the Newton’s algorithm for one optimization iteration

Profiling results for the benchmark problem on the ADCUS-Coprocessor architecture


Asip design framework
ASIP design framework Architecture

Satisfy: System performance requirements using minimum required implementation complexity

Emulations: Logarithmic number system (LNS) arithmetic

K integer bits and F fraction bits

[minimize]

LNS: advantage in cost, power consumption and speed, that increases as the word size decreases

Adjust the size of words (the #bits processed in a single instruction) using parametric simulation tests


Application heat regulation
Application: Heat Regulation Architecture

Figure: % of error for different control horizons


Heat regulation initial simulations
Heat Regulation - Initial Simulations Architecture

Using K=7, F=20 and CH=6


Word size reduction
Word size reduction Architecture

Figure: % of error for different values of F

Figure: Actuation/ Output (K=5, F=10 and CH=6)

  • Observations:

  • While the output is “far” from the set point, the behavior is close to optimal (full precision).

  • Low precision causes large errors in the controlled variable when close to the set point.


Reduced precision simulations
Reduced precision simulations Architecture

Using K=5, F=10 and CH=6

Using K=5, F=8 and CH=6


Hardware implementation
Hardware Implementation Architecture

  • Estimations for both 64-bit FP and 16-bit LNS circuits show:

  • The size required is about 17 times smaller in 16-bit LNS.

  • The clock cycle is at least 3.23 times faster in 16-bit LNS.

  • The proposed problem can be solved at sampling speeds as low as 32ms.

L. Bleris, J. Garcia, M. Arnold and M. Kothare, “Towards Embedded Model Predictive Control for System-On-a-Chip Applications”, Journal of Process Control, 16, 255-264, Mar. 2006.



Emulation results
Emulation Results Architecture

Switching between setpoints using MPC (solid line)

and a heuristic controller (dashed line).

Top plot: transient response of the concentration using

step response (dashed line), MPC I (thin line) and MPC II (solid line). Bottom plot: the actuation for the MPC II case.

L. Bleris, J. Garcia, M. Arnold and M. Kothare, “Model predictive hydrodynamic regulation of microflows”. Journal of Micromechanics and Microengineering, 16, 1792-1799, 2006.


Conclusions
Conclusions Architecture

  • S/W-H/W Co-Designed Embedded Controller

    • S/W & H/W are tailored to the particular family of problems

    • Bigger development effort

  • Application-Specific Processor

    • Accuracy tailored to the particular problem

    • Most efficient in terms of power consumption and performance

    • Once fabricated cannot be reconfigured

  • Embedded optimization and model based controllers:

    • can play a critical role in ensuring the proper functionality

    • desired performance of any device

  • Economic operating point of typical processes are close to constraints


Acknowledgements
Acknowledgements Architecture

  • Panagiotis Vouzis

  • Dr. Jesus Garcia

  • Prof. Kothare

  • Prof. Arnold

  • US National Science Foundation

    • CTS-9980781 (‘Engineering Microsystems: XYZ-on-a-chip’ program)

    • CTS-0134102 (CAREER program)

  • The Technology Collaborative

  • ADCUS, Inc.

    Thank you for your attention


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