(329c) Optcon – An Efficient Tool for Rapid Prototyping of Nonlinear Model Predictive Control Applications

OptCon – an Efficient Tool for Rapid Prototyping of Nonlinear Model Predictive Control Applications

Z. K. Nagy

Chemical Engineering Department, Loughborough University, Loughborough, LE11 3TU, United Kingdom, email: z.k.nagy@lboro.ac.uk

Nonlinear model predictive control is an optimization-based multivariable constrained control technique that uses a nonlinear dynamic process model for the prediction of the process outputs. At each sampling time the model is updated on the basis of new measurements and state variable estimates. Then the open-loop optimal manipulated variable moves are calculated over a finite prediction horizon with respect to some cost function, and the manipulated variables for the subsequent prediction horizon are implemented. Then the prediction horizon is shifted by usually one sampling time into the future and the previous steps are repeated. NMPC is one of the approaches which inherently can cope with process constraints, nonlinearities and different objectives formulated form economical or environmental considerations. Although the advantages of NMPC have been demonstrated through numerous simulation studies the gap between the number if simulation papers and actual practical implementations is significant. This gap is even more pronounced if consider real industrial applications. The talk will briefly asses the major implementation aspects of NMPC introducing the integral NMPC design concept. Figure 1 illustrates the NMPC pentagon, which constitutes the basis of the integral NMPC design. All sides of the pentagon have to be considered for successful practical implementation.

Fig.1. “NMPC Pentagon” that illustrates the main aspects to be considered in an integral design of a practical NMPC.

A Matlab toolbox will be illustrated which has been developed with the aim to provide a rapid prototyping tool for NMPC applications. The NMPC approach presented in this talk is a first principles model based approach that can be used for the solution of moving or shrinking horizon (batch) control problems. The NMPC tool developed includes a number of desirable features. In particular the NMPC setup can be done in Matlab^®  (The Mathworks Inc.) the most widely used modeling and control environment for control engineers. The model used in the controller has to be developed in the form of Simulink^® (The Mathworks Inc.) “mex S-function” using C. The S-function interface of the optimization tool provides convenient and fast connectivity with Matlab^®. The NMPC approach is based on a state-of-the-art large-scale nonlinear optimization solver (HQP), which offers one of the most efficient approaches, based on a multiple shooting algorithm, that exploits the special structure of optimization problem that arise in NMPC. In this algorithm the optimization horizon of interest is divided into a number of subintervals (stages) with local control parameterizations. The differential equations and cost on these intervals are integrated independently during each optimization iteration, based on the current guess of the control. The continuity/consistency of the final state trajectory at the end of the optimization is enforced by adding consistency constraints to the nonlinear programming problem. This multistage formulation is advantageous to the efficient application of the SQP-type solver in HQP, and often leads to faster solution of the optimization problem due to the better approximation of the Lagrangian Hessian of the nonlinear subproblems using low rank updates. HQP uses a sparse interior point algorithm for the efficient treatment of the linear-quadratic subproblems in the nonlinear SQP iterations. The main structure of the OptCon software is shown on Figure 2.

Fig. 2. Structure of the main components of the NMPC toolbox - OptCon

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The wide range of applicability of the NMPC tool, OptCon will be illustrated through a couple of examples. First, the application of OptCon to a laboratory four tank system will be illustrated briefly, which is the first practical application of a theoretically well founded NMPC approach (the so called quasi-infinite horizon NMPC), that guarantees stability. Next we illustrate how the same tool can be used for prototyping industrial NMPC applications and go from simulation studies to the actual practical tests within minutes. The potential advantages and disadvantages of the application of NMPC to an industrial batch polymerization reactor are outlined, in special focusing on the computational feasibility and robustness against numerical failures, using the NMPC tool developed. The quality of the product strongly depends on how tightly the temperature profile is tracked during the batch. Disturbances caused by the effects of exothermic reaction cause overshooting when classical cascade-PI control is used, with an increasing degradation in control performance when batch time is reduced. It is shown that NMPC can provide higher control performance for setpoint tracking. Additionally, simulations show that product quality can significantly decrease in case of certain disturbance scenarios. The NMPC approach proposed here is a hierarchical (two level) NMPC approach, in which a higher level NMPC controller reoptimizes on-line the setpoint, based on the desired end-point properties of the product. The setpoint is sent to a lower level, setpoint-tracking NMPC. The computational complexity and real-time feasibility of the two control problems are studied, and results show that with this approach good temperature tracking is achieved and the product quality at the end of the batch is well controlled.