52 resultados para optimal control design
em CentAUR: Central Archive University of Reading - UK
Resumo:
This paper introduces PSOPT, an open source optimal control solver written in C++. PSOPT uses pseudospectral and local discretizations, sparse nonlinear programming, automatic differentiation, and it incorporates automatic scaling and mesh refinement facilities. The software is able to solve complex optimal control problems including multiple phases, delayed differential equations, nonlinear path constraints, interior point constraints, integral constraints, and free initial and/or final times. The software does not require any non-free platform to run, not even the operating system, as it is able to run under Linux. Additionally, the software generates plots as well as LATEX code so that its results can easily be included in publications. An illustrative example is provided.
Resumo:
A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.
Resumo:
The frequency responses of two 50 Hz and one 400 Hz induction machines have been measured experimentally over a frequency range of 1 kHz to 400 kHz. This study has shown that the stator impedances of the machines behave in a similar manner to a parallel resonant circuit, and hence have a resonant point at which the Input impedance of the machine is at a maximum. This maximum impedance point was found experimentally to be as low as 33 kHz, which is well within the switching frequency ranges of modern inverter drives. This paper investigates the possibility of exploiting the maximum impedance point of the machine, by taking it into consideration when designing an inverter, in order to minimize ripple currents due to the switching frequency. Minimization of the ripple currents would reduce torque pulsation and losses, increasing overall performance. A modified machine model was developed to take into account the resonant point, and this model was then simulated with an inverter to demonstrate the possible advantages of matching the inverter switching frequency to the resonant point. Finally, in order to experimentally verify the simulated results, a real inverter with a variable switching frequency was used to drive an induction machine. Experimental results are presented.
Resumo:
This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.
Resumo:
This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.
Resumo:
This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.
Resumo:
This paper is concerned with the design of robust feedback H~-control systems for the control of the upright posture of paraplegic persons standing. While the subject stands in a special apparatus, stabilising torque at the ankle joint is generated by electrical stimulation of the paralyzed calf muscles. Since the muscles acting as actuators in this setup show a significant degree of nonlinearity, a robust H~-control design is used. The design approach is implemented in experiments with a paraplegic subject. The results demonstrate good performance and closed loop stability over the whole range of operation.
Resumo:
A novel algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimisation and Parameter Estimation (DISOPE) which has been designed to achieve the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimisation procedure. A method based on Broyden's ideas is used for approximating some derivative trajectories required. Ways for handling con straints on both manipulated and state variables are described. Further, a method for coping with batch-to- batch dynamic variations in the process, which are common in practice, is introduced. It is shown that the iterative procedure associated with the algorithm naturally suits applications to batch processes. The algorithm is success fully applied to a benchmark problem consisting of the input profile optimisation of a fed-batch fermentation process.
Resumo:
An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.
Resumo:
This paper uses genetic algorithms to optimise the mathematical model of a beer fermentation process that operates in batch mode. The optimisation is based in adjusting the temperature profile of the mixture during a fixed period of time in order to reach the required ethanol levels but considering certain operational and quality restrictions.
Resumo:
An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.