德国工业4.0原版

Model predictive control (MPC)
Modern, optimization-based control technique Successful applications in many industrial fields Can handle hard constraints on states and inputs Optimization of some performance criterion Applicable to nonlinear, MIMO systems
z
z
z
z
z
Energy and resource efficient, safe and reliable production process
Optimization-based control plays a key role in visionline
Part 1: A distributed economic MPC framework for Industry 4.0 Part 2: Distributed optimization for Industry 4.0
Economic MPC [Angeli et al. ’12]
Stage cost can be general cost function, need not be positive definite ⇒ Closed-loop system is not necessarily convergent Resulting questions:
k =0 x (t ) x (k |t )
∗
k =N
Basic MPC scheme
At each time t , solve finite horizon optimal control problem
state x input u t u ∗ (k |t )
Model predictive control
Industry 4.0 – Impact in Germany
Industry 4.0 – a hot topic in Germany
z
Most of the big companies in Germany consider Industry 4.0 as key vision
and contribute to its realization
z
Intense research activities in universities and other research institutions Drastically increasing number of publications in recent years Large amount of funding by the German government
z
Many opportunities for control field
z
Individualized, modularized, flexible production Manufacturing chain consisting of self-configuring, real-time optimized components Interaction between individual components by means of digital, networked communication
(x , u )
A system is optimally operated at steady-state if for each feasible state and input sequences x(·) and u(·) the following holds:
T −1
lim inf
T →∞ k =0
Industry 4.0: Challenges and opportunities for optimization-based control
Frank Allgöwer
Institute for Systems Theory and Automatic Control University of Stuttgart, Germany
What is the optimal operational regime (steady-state, periodic)? How to handle constraints on average quantities of states and inputs? Distributed implementation of economic MPC schemes?
Mathias Bürger (Robert Bosch GmbH)
Matthias Müller (IST, Stuttgart)
Model predictive control
Model predictive control (MPC)
Modern, optimization-based control technique Successful applications in many industrial fields Can handle hard constraints on states and inputs Optimization of some performance criterion Applicable to nonlinear, MIMO systems
Standard MPC problem formulation
N −1
min
u(t ) k =0
(x (k |t ), u (k |t )) + V f (x (N |t )) k ∈ I[0,N −1]
s.t.
x (0|t ) = x (t ), x (k + 1|t ) = f (x (k |t ), u (k |t )), (x (k |t ), u (k |t )) ∈ Z, x (N |t ) ∈ Xf k ∈ I[0,N ]
Model predictive control (MPC)
Modern, optimization-based control technique Successful applications in many industrial fields Can handle hard constraints on states and inputs Optimization of some performance criterion Applicable to nonlinear, MIMO systems
(x (k ), u (k )) ≥ (x ∗ , u ∗ ). T
Optimal steady-state operation is closely related to a dissipativity condition!
Definition - Dissipativity [Willems ’72, Byrnes & Lin ’94]
Contribution of systems perspective on Industry 4.0 Rigorous mathematical approach for certification and guarantees Development of methods and tools for - analysis - distributed controller design - systems design
z
Intense research activities in universities and other research institutions Drastically increasing number of publications in recent years Large amount of funding by the German government
Economic model predictive control
Manufacturing industry: cost efficient scheduling of production process (especially important for vision of “smart factory”) Maximization of product in process industry Minimization of energy consumption in refrigeration system ⇒ Setpoint stabilization is not primary control objective
z
z
Industry 4.0 – Impact in Germany
Industry 4.0 – a hot topic in Germany
z
Most of the big companies in Germany consider Industry 4.0 as key vision
and contribute to its realization
Most results in MPC literature: classical control objective of setpoint stabilization is considered ⇒ Basic assumption: stage cost is positive definite w.r.t. setpoint to be stabilized However: different control objective is of interest in many applications
Model predictive control - problem setup