Model predictive control

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The model predictive control , mostly called Model Predictive Control ( MPC ) or Receding Horizon Control ( RHC ), is a modern method for the predictive control of complex, i. d. R. multi-variable processes .

functionality

Control behavior of a time-discrete MPC model

In the MPC, a time-discrete dynamic model of the process to be controlled is used to calculate the future behavior of the process as a function of the input signals. This enables the calculation of the optimal input signal - in terms of a quality function - which leads to optimal output signals. Input, output and status restrictions can be taken into account at the same time. While the model behavior is predicted up to a certain time horizon N, usually only the input signal u is used for the next time step and then the optimization is repeated. The optimization is carried out in the next time step with the then current (measured) state, which can be understood as a feedback and turns the MPC into a regulation in contrast to optimal controls. This allows disturbances to be taken into account, but also requires considerable computing power.

${\ displaystyle {\ text {Determine}} \; u = \ arg \ min _ {u} J (x (0), u)}$

${\ displaystyle \ mathrm {udN} \; J (x (0), u) = \ sum _ {k = 0} ^ {N} (\ | x (k) \ | _ {Q} + \ | u ( k) \ | _ {R}), \ quad x (k) \ in {\ mathcal {X}}, \; u (k) \ in {\ mathcal {U}}}$

The process models can be of various forms, e.g. B. Transfer function or state space representation. In addition to the mostly linear process models, artificial neural networks are occasionally used to create a process model. These controllers then belong to the class of NMPC ( Nonlinear Model Predictive Control ), as do forms of adaptive controllers .

application areas

In contrast to many other modern control methods, MPC has already been widely used in industry due to its ability to explicitly take restrictions into account. MPC controllers are preferably used in process engineering processes (including combustion processes in power plants , waste incineration plants , paper machines , rolling mills and cement works ), in which classic controllers (P, D, PID controllers ) and fuzzy controllers achieve insufficient control quality , and the relevant system dynamics are slow enough to be able to carry out an optimization in each sampling step. MPCs often also serve as higher-level controls for basic automation, e.g. B. in the form of a cascade as a manipulated variable of a PID controller.

Process engineering processes are often automated by process control systems . The optimization algorithm of a model predictive control is i. d. Usually not carried out within the process-related components / controller, but implemented in an external process computer that z. B. communicates with the control system via OPC . This is due to the computing power required to calculate the algorithm and the rather low computing capacity of the process-related controller. The computing power required is also dependent on the number of inputs and outputs of the process. One goal is to integrate MPC into the process-related components and thus avoid costs for the integration of special hardware. This is particularly promising and useful for processes with a small number of inputs and outputs. In addition to the 'online' calculation of the algorithm in the controller, another approach is the calculation of all solutions to an optimization problem in advance. These precalculated results are then stored in the controller and searched during operation.

variants

Move blocking
Explicit MPC
Minimum time MPC
Infinite Horizon MPC
Nonlinear MPC
Robust MPC
Economic MPC
Multiplexed MPC

literature

Rainer Dittmar, Bernd-Markus Pfeiffer: Model-based predictive control: An introduction for engineers (2004), Oldenbourg ISBN 3486275232
Jan M. Maciejowski: Predictive Control with Constraints (2002), Prentice Hall, ISBN 0-201-39823-0
M. Morari and NL Ricker: Model Predictive Control Toolbox User's Guide (1995), The Mathworks Inc.
M. Kvasnica, I. Rauova, and M. Fikar: Automatic code generation for real-time implementation of Model Predictive Control , in: Computer-Aided Control System Design (CACSD), 2010 IEEE International Symposium on, 2010, p. 993– 998.
M. Rau: Nonlinear model-based predictive control based on adaptive state space models (PDF file; 4.75 MB)

Individual evidence

^ Lars Grüne, Jürgen Pannek: Nonlinear Model Predictive Control. Accessed January 30, 2020 .
^ KV Ling, JM Maciejowski, AG Richards, B.-F. Wu: Multiplexed Model Predictive Control . In: arXiv: 1101.2785 [cs, math] . January 14, 2011, arxiv : 1101.2785 .

[1] Lars Grüne, Jürgen Pannek: Nonlinear Model Predictive Control. Accessed January 30, 2020 .

[2] KV Ling, JM Maciejowski, AG Richards, B.-F. Wu: Multiplexed Model Predictive Control . In: arXiv: 1101.2785 [cs, math] . January 14, 2011, arxiv : 1101.2785 .