H0K03a : Advanced Process Control Model-based Predictive Control 1 : Introduction Bert Pluymers Prof. Bart De Moor Katholieke Universiteit Leuven, Belgium Faculty of Engineering Sciences Department of Electrical Engineering (ESAT) Research Group SCD-SISTA H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Overview • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation • MPC 1 : Introduction • MPC Basics • MPC 2 : Dynamic Optimization • MPC 3 : Stability • MPC 4 : Robustness • Industry Speaker : Christiaan Moons (IPCOS) (november 3 rd ) S ignal processing I dentification S ystem T heory 1 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Overview • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation Lesson 1 : Introduction • MPC Basics • Motivating example • MPC Paradigm • History • Mathematical Formulation • MPC Basics S ignal processing I dentification S ystem T heory 2 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation Consider a linear discrete-time state-space model • MPC Basics called a ‘ double integrator ’. We want to design a state feedback controller that stabilizes the system (i.e. steers it to x=[0; 0]) starting from x=[1; 0], without violating the imposed input constraints S ignal processing I dentification S ystem T heory 3 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation Furthermore, we want the controller to lead to a • MPC Basics minimal control ‘cost’ defined as with state and input weighting matrices A straightforward candidate is the LQR controller, which has the form S ignal processing I dentification S ystem T heory 4 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History LQR controller • Mathematical Formulation • MPC Basics 1 0.5 x k,1 0 -0.5 0 50 100 150 200 250 300 k 10 0 u k -10 -20 -30 0 50 100 150 200 250 300 S ignal processing k I dentification S ystem T heory 5 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History LQR controller with clipped inputs • Mathematical Formulation 1 • MPC Basics 0.5 x k,1 0 -0.5 -1 0 50 100 150 200 250 300 k 0.15 0.1 0.05 u k 0 -0.05 -0.1 0 50 100 150 200 250 300 S ignal processing k I dentification S ystem T heory 6 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History LQR controller with R=100 • Mathematical Formulation 1 • MPC Basics 0.5 x k,1 0 -0.5 0 50 100 150 200 250 300 k 0.1 0.05 u k 0 -0.05 -0.1 0 50 100 150 200 250 300 S ignal processing I dentification k S ystem T heory 7 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
Motivating Example • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation waste gas • MPC Basics F T Cracking P Furnace Feed H condenser EDC L EDC / VC / HCl superheater evaporato T r P F Fuel gas Systematic way to deal with this issue… ? S ignal processing I dentification S ystem T heory 8 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
MPC Paradigm • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation • MPC Basics Process industry in ’70s : how to control a process ??? S ignal processing I dentification and… easy to understand (i.e. teach) and implement ! S ystem T heory 9 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
MPC Paradigm • Overview • Motivating Example • MPC Paradigm → Modelbased Predictive Control (MPC) • History • Mathematical Formulation • MPC Basics • Predictive : use model to optimize future input sequence S ignal processing • Feedback : incoming measurements used to compensate for I dentification inaccuracies in predictions and unmeasured disturbances S ystem T heory 10 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
MPC Paradigm • Overview • Motivating Example • MPC Paradigm MPC has earned its place in the control hierarchy… • History • Mathematical Formulation • MPC Basics • Econ. Opt. : optimize profits using market and plant information (~day) • MPC : steer process to desired trajectory (~minute) • PID : control flows, temp., press., … towards MPC setpoints (~second) S ignal processing I dentification S ystem T heory 11 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
History • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation Before 1960’s : • MPC Basics • only input/output models, i.e. transfer functions, FIR models • Controllers : • heuristic (e.g. on/off controllers) • PID, lead/lag compensators, … • mostly SISO • MIMO case : input/output pairing, then SISO control S ignal processing I dentification S ystem T heory 12 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
History • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation Early 1960’s : Rudolf Kalman • MPC Basics • Introduction of the State Space model : • notion of states as ‘internal memory’ of the system • states not always directly measurable : ‘Kalman’ Filter ! • afterwards LQR (as the dual of Kalman filtering) • LQG : LQR + Kalman filter • But LQG no real succes in industry : • constraints not taken into account • only for linear models • only quadratic cost objectives S ignal processing I dentification • no model uncertainties S ystem T heory 13 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
History • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation During 1960’s : ‘Receding Horizon’ concept • MPC Basics • Propoi, A. I. (1963). “ Use of linear programming methods for synthesizing sampled-data automatic systems ”. Automatic Remote Control, 24(7), 837 – 844 . • Lee, E. B., & Markus, L. (1967). “ Foundations of optimal control theory ” . New York: Wiley. : “… One technique for obtaining a feedback controller synthesis from knowledge of open-loop controllers is to measure the current control process state and then compute very rapidly for the open- loop control function. The first portion of this function is then used during a short time interval, after which a new measurement of the function is computed for this new measurement. The procedure is then repeated. …” S ignal processing I dentification S ystem T heory 14 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
History • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation During 1960’s : ‘Receding Horizon’ concept • MPC Basics S ignal processing I dentification S ystem T heory 15 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
History • Overview • Motivating Example • MPC Paradigm • History • Mathematical Formulation 1970’s : 1 st generation MPC • MPC Basics • Extension of the LQR / LQG framework through combination with the ‘receding horizon’ concept • IDCOM (Richalet et al., 1976) : • IR models • quadratic objective • input / output constraints • heuristic solution strategy • DMC (Shell, 1973) : • SR models • quadratic objective • no constraints S ignal processing • solved as least-squares problem I dentification S ystem T heory 16 A utomation H0k03a : Advanced Process Control – Model-based Predictive Control 1 : Introduction bert.pluymers@esat.kuleuven.be
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