Predicting the Future of Model Predictive Control Manfred Morari In Honor of Professor David Clarke Oxford, January 9, 2009 Automatic Control Laboratory, ETH Zürich www.control.ethz.ch
Model Predictive Control past future Predicted outputs Manipulated (t+k) u Inputs t+p t t+1 t+m 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, Tu � s; Generalized Predictive Control. Automatica
Clarke, Mohtadi & Tu � s Generalized Predictive Control Automatica: 3 rd 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, Tu � s; 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, Tu � s; 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: 2 nd 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, Tu � s; 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 on 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, Tu � s ; 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 Double-Click on picture to start AIChE CAST Award 2007 movie. h � p://www.castdiv.org/spring08.htm#co1
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 so � ware is faster • � Special MPC algorithms for fast systems
What happened? • � Computers are faster • � Optimization so � ware is faster • � Special MPC algorithms for fast systems
Speedup of so � ware 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 Cu � ing Planes x 50 Source: Bixby, Gu, Rothberg, Wunderlich 2004
What happened? • � Computers are faster • � Optimization so � ware is faster • � Special MPC algorithms for fast systems
Receding Horizon Control On-Line Optimization Optimization Obtain U * (x) Problem plant state x control u 0 * output y Plant Model Predictive Control (MPC)
Receding Horizon Control O � -Line Optimization off-line Explicit Solution Parametric Optimization (=Look-Up Table) Solution of plant state x Bellman equation control u * output y Plant Seron, De Doná and Goodwin, 2000 Explicit MPC Johansen, Peterson and Slupphaug, 2000 Bemporad, Morari, Dua and Pistokopoulos, 2000
Explicit MPC
Explicit MPC
Multi-parametric controllers 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
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 : Without computing J � ! J *( x )
Suboptimal problem Goal: Find simple function such that • � Stability : • � Invariance : All ‘nearby’ functions are Lyapunov • � Performance : Without computing J � ! Level sets are invariant
Beneath/Beyond and Double Description Beneath/Beyond : Inside to out [C.N. Jones, M. Baric and M. Morari, 2007] Double Description : Outside to in • � Often generates simpler controllers [C.N. Jones and M. Morari, 2008]
Polyhedral approximation of convex problems Parametric Parametric Parametric quadratic geometric second-order cone programming programming 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 thro � le 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 Di � erential 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
MPC Research Theory Computation Applications
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