Assessment and Future Directions of Nonlinear Model Predictive ...

Application of the NEPSAC Nonlinear Predictive Control Strategy 5053 EPSAC Model Based Predictive Control StrategyAmong the diversity of control engineering principles available today, MPC hasclearly some useful characteristics to tackle above mentioned challenges: the latestMPC-versions can deal with nonlinear models, it is a multivariable controlstrategy and it takes into account the system constraints aprioriby using constrainedoptimization methods. In this application we used our in-house EPSACpredictive control method, which has been originally described in [2, 3] and hasbeen continuously improved over time [5]. The latest version, NEPSAC, is anonlinear predictive controller which is essentially characterized by its simplicitysince it consists of repetitive application of the basic linear EPSAC algorithmduring the controller sampling interval. It leads in an iterative way, after convergence,to the optimal solution for the underlying nonlinear problem.Many powerful NMPC (Nonlinear Model based Predictive Control) strategiesexists today; they have been widely published in the control literature, e.g.[1]. The advantages of NEPSAC compared to other NMPC methods are mainlyfrom a practical point-of-view: the approach provides a NMPC algorithm whichis quite suitable for real-life applications as it does not require significant modificationof the basic EPSAC software and as it is computationally simple andfast compared to other NMPC strategies [7]. The shortcomings are mainly froma theoretical point-of-view: convergence of the iterative strategy and closed-loopstability could not (yet) be proven in a formal theoretical way, although numeroussimulation studies and several real-life applications have resulted in verysatisfying performance.3.1 Process ModelThe basic control structure is illustrated in Fig. 2. For use in the MPC strategy,the process is modelled asy(t) =x(t)+n(t) (1)with y(t) = process output (TC temperature measurement); u(t) = process input(voltage to SCR power pack); x(t) = model output; n(t) = process/modeldisturbance. The model (1) is presented for a SISO-process (Single Input SingleOutput), i.e. only 1 TC sensor and 1 SCR control input. This is done for clarityonly. The (straightforward) extension to MIMO-systems, in this case a 4x4system, is presented in detail in [5].The process disturbance n(t) includes all effects in the measured outputy(t) which do not come from the model output x(t). Thisisafictitious (nonmeasurable)signal. It includes effects of deposition, gas flow, measurement noise,model errors, ... These disturbances have a stochastic nature with non-zero averagevalue. They can be modelled by a colored noise process:n(t) =C(q −1 )/D(q −1 ) e(t) (2)