A Model Predictive Control software: MPC@CB Jun QIAN 1, 2 , Pascal DUFOUR 1,3 , Madiha NADRI 1 1 Laboratory of Process Control and Chemical Engineering (LAGEP), UMR5007, CNRS, Universit ´ e Claude Bernard Lyon 1 2 Acsyst ` eme company (IT and Control engineering), Rennes, France 1, 2 Emails: jun.qian@acsysteme.com or qian@lagep.univ-lyon1.fr; dufour@lagep.univ-lyon1.fr; nadri@lagep.univ-lyon1.fr; 3 Project leader and contact. Software website: http://MPCatCB.univ-lyon1.fr Main features of the MPC@CB software ◮ MPC@CB is a control software for dynamic systems based on any kind of model: SISO or MIMO (S=single, M=multiple), linear or nonlinear, time variant or time invariant, with ordinary differential equations (ODE) and/or partial differential equations (PDE). ◮ MPC@CB is a model predictive control (MPC) strategy for solving an optimal control problem (trajectory tracking, processing time minimization, any user defined criteria ...) with input constraints and with or without output constraints. ◮ Open loop or PID may also be applied by the software before using MPC@CB (to compare these different control approaches). ◮ A software model based sensor (observer) can be introduced. ◮ Industrial application domains: chemistry/chemical engineering, electrical engineering, food, materials, mechanics, pharmaceuticals,... ◮ MPC@CB may be used for simulation (training) or real time application. MPC: general framework ◮ MPC scheme ◮ MPC algorithm First, the user defines its own optimal control problem (reference trajectory tracking, energy minimization, velocity maximization, ...), and the input/output constraints. Secondly, he defines the model and tunes the MPC controller. Then, at each current sampling time k, a MPC software: ◮ Updates the plant measurements needed by the control loop. ◮ Computes a future optimal control actions sequence: { ˜ u (k |k ), ˜ u (k + 1|k ),..., ˜ u (k + N p - 1|k )} by solving the constrained optimization problem, including the cost of future control actions and the cost of future deviations from a reference behaviour. ◮ Applies the first movement of the optimal control sequence on the process at the next sampling time. These operations are repeated at next time k + 1. MPC@CB: specific control approach used ◮ Linearized IMC-MPC structure MPC@CB is based on an internal model control (IMC) structure where: ◮ The nonlinear model S 0 is solved off-line. ◮ The time-varying linearized model S TVL (obtained from S 0 ) is solved on-line during the optimization task. ◮ The off-line open loop results are used on-line for the correct closed loop optimal constrained tuning of the control action. ◮ Formulation of the optimization problem solved in a MPC approach                      min p J tot = J (p )+ J ext (p ) J (p )= ∑ k +N p j =k +1 g (y ref (j ), Δy m (j ), Δu (p (j )), e (k )) J ext (p )= ∑ k +N p j =k +1 ( ∑ N c i =1 w i max 2 (0, c i (y ref (j ), Δy m (j ), Δu (p (j )), e (k )))) p : unconstrained input parameter c i : output constraints for the controlled variables Input constraints handling: hyperbolic transformation Ouput constraints handling: exterior penalty method (1) Stage of development for MPC@CB ◮ History: created in 2007, under Matlab, with GUI ◮ Today: a standalone application without Matlab is available Case study (CSTR): model A continuous stirred tank reactor (CSTR) is a nonlinear chemical process with a simple controllable input T c (the temperature of cooling jacket, K ) and a simple output c A (concentration of A, mol /m 3 ). The first order, exothermic reaction A → B is described as follows: (Σ)      ˙ c A (t )= q V (c f A - c A (t )) - k 0 exp ( - ( E R ) /T (t ) ) c A (t ) ˙ T (t )= q V (T f - T (t )) + ΔH ρC p k 0 exp ( - ( E R ) /T (t ) ) c A + UA ρVC p (T c - T (t )) y (t )= c A (t ) (2) The objective of this application is to use MPC@CB (with or without the output constraint y > y min = 0.87) for the set-point tracking of a reference value 0.86, and the input constraints: 250K < T c < 320K . Case study (CSTR): simulation results ◮ without the output constraint ◮ optimal input applied ◮ trajectory tracking ◮ with the output constraint: y > y min = 0.87 ◮ optimal input applied ◮ trajectory tracking Conclusion ◮ MPC@CB is easily tunable for any new dynamic process. ◮ The specified user defined constrained control objectives are well achieved by the online closed loop control with MPC@CB. ◮ With the off-line and on-line IMC-MPC structure, the on-line computational time of optimization is decreased by MPC@CB. ◮ More case studies are discussed on the website. ◮ MPC@CB is available: short time evaluation, commercial licence or embedded in a complete turnkey solution for the customer. References [1] N. Daraoui, P. Dufour, H. Hammouri, A. Hottot, Model predictive control during the primary drying stage of lyophilisation, Control Engineering Practice, 2010, 18(5), pp. 483-494. [2] I. Bombard, B. Da Silva, P. Dufour and P. Laurent, Experimental predictive control of the infrared cure of a powder coating: a non-linear distributed parameter model based approach, Chemical Engineering Science Journal, 2010, 65(2), pp. 962-975. [3] P. Dufour, Y. Tour´ e, D. Blanc, P. Laurent,On nonlinear distributed parameter model predictive control strategy: On-line calculation time reduction and application to an experimental drying process, Computers and Chemical Engineering, 2003, 27(11), pp.1533-1542. Contact for the software MPC@CB http://MPCatCB.univ-lyon1.fr/ MPCatCB@univ-lyon1.fr