Model Predictive Control for Embedded Applications

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Model Predictive Control for Embedded
Applications Leonidas G. Bleris Panagiotis
Vouzis, Mark Arnold, and Mayuresh V.
Kothare 2006 AIChE Annual MeetingSan Francisco,
CA
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Introduction

• Model Predictive Control
• Theory
• MPC for Portable Devices
• Implementation Pathways
• Applications
• Concluding Remarks

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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

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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)
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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
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Receding horizon solution
Disturbances
Parameters
Umpc
System
Output
Uinitial
Future
Past
Set-point
Projected output
Manipulated input
k
K1
K2
K3
Km-1
Prediction Horizon
Control Horizon
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Models
Model Type Origin Linear/Nonlinear Stable/Unstable
Differential Equations Physics L/NL S/U
State-Space Physics/Data L/NL S/U
Transfer Functions Physics/Data L S/U
ARMAX/NARMAX Data L/NL S/U
Convolution Data L S
Other Data L/NL S/U
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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
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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

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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 Newtons algorithm, the number of
  operations is 12(n36n210n), 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!
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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

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Biomedical Applications
R. Dorf and R. Bishop, Modern Control Systems,
Addison Wesley, 7th edition, 1995.
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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 US2.4 billion for 2004 with
  expected annual growth of 32
• Neuronal prosthetics market, at US2.2 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

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Automotive
Economist, September 2006
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Wind turbines
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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
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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

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S/W-H/W Co-Design Approach
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MPC formulation

• The optimization problem
• State-Space model of a system
• Results to

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Computational Issues in MPC

• Using Newton's method
• We get
• where
• Abundant matrix operations

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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.
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Profiling and Timing Results of the
ADCUS-Coprocessor Architecture
The clock cycles required by each function of the
Newtons algorithm for one optimization iteration
Profiling results for the benchmark problem on
the ADCUS-Coprocessor architecture
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ASIP design framework
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

• Satisfy System performance requirements using
  minimum required implementation complexity

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Application Heat Regulation
Figure of error for different control horizons
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Heat Regulation - Initial Simulations
Using K7, F20 and CH6
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Word size reduction
Figure of error for different values of F
Figure Actuation/ Output (K5, F10 and CH6)

• 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.

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Reduced precision simulations
Using K5, F10 and CH6
Using K5, F8 and CH6
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Hardware Implementation

• 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.
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Hydrodynamic Regulation Case
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Emulation Results
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.
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Conclusions

• 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

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Acknowledgements

• 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