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sigpromu-org-document-634 - Nonlinear Model Predictive...

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Nonlinear Model Predictive Control of an Inverted Pendulum Adam Mills, Adrian Wills, Brett Ninness Abstract — In this paper, nonlinear model predictive control is applied to an inverted pendulum apparatus. The sample interval for control calculations is 25 milli-seconds and the associated non-convex constrained optimisation problem in- volves 61 -variables with 241 -constraints. Despite this being a challenging problem, it was solved on-line using a standard sequential quadratic programming approach on a modest hardware platform. The efficacy of the control algorithm is validated via experimental results. I. INTRODUCTION Nonlinear Model Predictive Control (NMPC) is an attrac- tive strategy for controlling complex systems [1]. It has been used for decades within process control industries [2], [3], because it offers good dynamic performance while ensuring operation within certain physical limits. This latter feature enables plant operators to run the plant near constraint boundaries, which can increase productivity and reduce product quality variation [2], [3]. However, a fundamental difficulty of this NMPC approach is that the implementation platform must be capable of solving a constrained optimisation problem within a specified time limit. This time decreases as the speed of the dynamics to be controlled increases. As a result, the implementation of NMPC has to date been generally limited to plants with slow or otherwise very simple dynamics so that the time constraints in computing a solution are relaxed. Surmounting this difficulty of computational overhead to achieve the benefits of Model Predictive Control for linear systems has recently attracted significant research attention [4], [5], [6], [7]. A similar trend is emerging for NMPC applications. For example, [8] applies NMPC to prevent the flooding of of a river system, where a sample time of 5 minutes is used. In [9] NMPC is applied to the problem of normalising the blood glucose levels in the critically ill. This application has a sample time of 5 minutes which resolves some of the issue of computation time. NMPC is applied to maximising the production rate of E. Coli in [10]. Here, online optimisation is eschewed in favour of a less computationally intensive control vector parametrisation method. NMPC is applied to Planar Vertical Take-Off and Landing (PVTOL) aircraft in [11] by using the structure of the model to convert a non-convex optimisation problem into two convex problems of lesser dimension. Adam Mills, Adrian Wills and Brett Ninness are with the School of Electrical Engineering and Com- puter Science, University of Newcastle, Callaghan, NSW, 2308, Australia [email protected] , [email protected] , [email protected] These applications have either slow dynamics which makes computation time less critical or use a simplified model to lessen the computation load. However, NMPC has also been applied to systems with fast dynamics.
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