Predicting the Future of Model Predictive Control Manfred Morari - - PowerPoint PPT Presentation

Automatic Control Laboratory, ETH Zürich

www.control.ethz.ch

Predicting the Future of Model Predictive Control

Manfred Morari

In Honor of Professor David Clarke Oxford, January 9, 2009

Model Predictive Control

Predicted outputs Manipulated (t+k) u Inputs t t+1 t+m t+p

future past

t+1 t+2 t+1+m t+1+p

• Determine state x(t)
• Determine optimal sequence of inputs over horizon
• Implement first input u(t)
• Wait for next sampling time; t:= t +1

Outline

• History
• Evolution
• Future

The History of MPC

Who invented predictive control? God ... Predictive control is a discovery, not an invention, ... But God need prophets. IFAC Congress Munich, 1987

The Evolution of MPC Milestones (personal)

• ~1980 Seminar by Haydel and Pre at

U.Wisconsin from Shell on work by/with Cutler and Ramaker

Cutler & Ramaker, 1979

Cutler & Ramaker, 1979

The Evolution of MPC Milestones (personal)

• ~1980: Seminar by Haydel and Pre at

U.Wisconsin from Shell on work by/with Cutler and Ramaker

• Early 1980s: Work with Garcia on Internal

Model Control

Work with Carlos Garcia

IEC Top ten cited article (since 1975)

The Evolution of MPC Milestones (personal)

• ~1980: Seminar by Haydel and Pre at

U.Wisconsin from Shell on work by/with Cutler and Ramaker

• Early 1980s: Work with Garcia on Internal

Model Control

• 1987: Clarke, Mohtadi, Tus; Generalized

Predictive Control. Automatica

Clarke, Mohtadi & Tus Generalized Predictive Control

Automatica: 3rd most cited article ever

The Evolution of MPC Milestones (personal)

• ~1980: Seminar by Haydel and Pre at

U.Wisconsin from Shell on work by/with Cutler and Ramaker

• Early 1980s: Work with Garcia on Internal

Model Control

• 1987: Clarke, Mohtadi, Tus; Generalized

Predictive Control. Automatica

• 1993: Rawlings & Muske; Stability of

Receding Horizon Control. IEEE-TAC

Rawlings & Muske Stability with Constraints

The Evolution of MPC Milestones (personal)

• ~1980: Seminar by Haydel and Pre at

U.Wisconsin from Shell on work by/with Cutler and Ramaker

• Early 1980s: Work with Garcia on Internal Model

Control

• 1987: Clarke, Mohtadi, Tus; Generalized

Predictive Control. Automatica

• 1993: Rawlings & Muske; Stability of Receding

Horizon Control. IEEE-TAC

• 2000: Mayne, Rawlings, Rao, Scokaert; MPC:

Stability & Optimality. Automatica

Mayne, Rawlings, Rao & Scokaert

Automatica: 2nd most cited article ever

The Evolution of MPC Milestones (personal)

• ~1980: Seminar by Haydel and Pre at U.Wisconsin on

work with Cutler and Ramaker

• Early 1980s: Work with Garcia on Internal Model

Control

• 1987: Clarke, Mohtadi, Tus; Generalized Predictive
• Control. Automatica
• 1993: Rawlings & Muske; Stability of Receding Horizon
• Control. IEEE-TAC
• 2000: Mayne, Rawlings, Rao, Scokaert; MPC: Stability &
• Optimality. Automatica
• 2003: Qin & Badgwell; Survey of Industrial MPC Techn.

Control Eng. Practice

Qin & Badgwell MPC Vendor Applications

Impact of Automation

• n Industrial Processes
• An emphasis on reducing operators in process plants
• A telling metric: "loops per operator"
• United States refining industry data:

– 1980: 93,000 operators, 5.3 bbl production – 1998: 60,000 operators, 6.2 bbl production (U.S. Bureau of the Census, 1999)

Source: T. Samad, Honeywell Laboratories, ESCAPE-11

Model Predictive Control

A Singular Success Story

• Impact on Academic Research
• Impact on Industrial Automation

Top ten cited articles in Automatica

#2 Constrained MPC: Stability & Optimality Mayne, Rawlings, Rao, Scokaert; 2000 #3 Generalized Predictive Control Clarke, Mohtadi, Tus; 1987 #7 MPC: Theory and Practice – A Survey Garcia, Pre, Morari; 1989 #9 Control of Systems Integrating Logic, Dynamics and Constraints Bemporad, Morari; 1999

• B. Erik Ydstie

AIChE CAST Award 2007

hp://www.castdiv.org/spring08.htm#co1

Double-Click on picture to start movie.

When the facts change, I change my mind. What do you do, Sir?

John Meynard Keynes

Outline

• History
• Evolution
• Future

The Past

Nonlinear Model Predictive Control Workshop Frank Allgöwer, Alex Zheng Ascona, 1998

Dominated by Process Control

The Present

Lalo Magni, Davide Raimondo, Frank Allgöwer

Process Control has almost disappeared

Applications in Automotive

ETH, November 2008

• Model Predictive Control of engine idle speed
• Preview control of boosted gasoline engines
• Optimal and predictive control of Hybrid Electric Vehicles

Applications in Power Electronics

Applications in Power Electronics

What happened?

• Computers are faster
• Optimization soware is faster
• Special MPC algorithms for fast systems

What happened?

• Computers are faster
• Optimization soware is faster
• Special MPC algorithms for fast systems

Speedup of soware for MIP in the last 15 years

Linear Program x 1000 Integer Program x 100 – 1000 Computers x 1000 Overall x 100 million Integer Programming

Preprocessing x 2 Heuristics x 1.5 Cuing Planes x 50

Source: Bixby, Gu, Rothberg, Wunderlich 2004

What happened?

• Computers are faster
• Optimization soware is faster
• Special MPC algorithms for fast systems

Obtain U*(x) Plant

• utput y

plant state x control u0*

Receding Horizon Control On-Line Optimization

Optimization Problem Model Predictive Control (MPC)

Parametric Optimization Explicit Solution Plant

• utput y

plant state x control u* (=Look-Up Table)

Receding Horizon Control O-Line Optimization

• ff-line

Seron, De Doná and Goodwin, 2000 Johansen, Peterson and Slupphaug, 2000 Bemporad, Morari, Dua and Pistokopoulos, 2000

Explicit MPC Solution of Bellman equation

Explicit MPC

Explicit MPC

Pros

– Easy to implement – Fast on-line evaluation – Analysis of closed-loop system possible

Challenges

– Number of controller regions can become large – Computation time may become prohibitive – Numerics

Multi-parametric controllers

Outline

• History
• Evolution
• Future

Research Directions

• 1. Reduce complexity of online optimization

– Rao, Wright, Rawlings, 1998 – Diehl, Björnberg, 2004 – Wang, Boyd, 2007

• 3. Reduce complexity of explicit solution

(i.e., number of regions)

– Jones, Baric, Morari, 2007 – Lincoln, Rantzer, 2006 – Bemporad, Filippi, 2004 – Johansen, Grancharova, 2003

• 4. Combination of 1. and 2.

– Panocchia, Rawlings, Wright, 2006 – Zeilinger, Jones, Morari, 2008

Optimal problem

• J* is a convex Lyapunov function => Stability
• Optimal control law is invariant

– Feasible for all time

• Optimal performance is satisfactory

Suboptimal problem

Goal: Find simple function such that

• Stability :
• Invariance :
• Performance :

J*(x) Without computing J!

Suboptimal problem

Goal: Find simple function such that

• Stability :
• Invariance :
• Performance :

Without computing J! Level sets are invariant All ‘nearby’ functions are Lyapunov

Beneath/Beyond and Double Description

Double Description : Outside to in

• Often generates simpler controllers

Beneath/Beyond : Inside to out

[C.N. Jones and M. Morari, 2008] [C.N. Jones, M. Baric and M. Morari, 2007]

Polyhedral approximation of convex problems

Parametric quadratic programming Parametric geometric programming Parametric second-order cone programming

Facts about MPT

13,000 downloads in 5+ years

Rated 4.5 / 5 on mathworks.com

Applications at ETH

50 kHz DC/DC converters (STM)

[Mariethoz et al 2008]

40 kHz Direct torque control (ABB)

[Papafotiou 2007]

10 kHz Voltage source inverters

[Mariethoz et al 2008]

200 Hz Electronic throle control (Ford)

[Vasak et al 2006]

50 Hz Traction control (Ford)

[Borrelli et al 2001]

30 Hz Autonomous vehicle steering (Ford)

[Besselmann et al 2008]

25 Hz Dierential gearbox with backlash

[Rostalski 2007]

2 Hz Adaptive cruise control (Daimler-Chrysler)

[Moebus et al 2003]

0.002 Hz Integrated room automation (Siemens)

[Oldewurtel et al 2008]

Applications at Ford Hybrid Vehicles

Kolmanovsky, 2008

Applications at Ford Hybrid Vehicles

Kolmanovsky, 2008

MPC Research Outlook

• Robustness
• Stochastic systems
• Adaptive MPC
• Switched / hybrid systems
• On-line/o-line computation,

complexity reduction

• Hierarchical / decentralized structure

Computation MPC Research Applications Theory