modelpredictivecontrol (MPC) is a favored method for handling constrained linear control problems. Normally, the MPC optimization problem is solved on-line, but in ‘explicit MPC’ an explicit precomputed feedback l...
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modelpredictivecontrol (MPC) is a favored method for handling constrained linear control problems. Normally, the MPC optimization problem is solved on-line, but in ‘explicit MPC’ an explicit precomputed feedback law is used for each region of active constraints (Bemporad et al., 2002). In this paper we make a link between this and the ‘self-optimizing control’ idea of finding simple policies for implementing optimal operation. The ‘nullspace’ method (Alstad and Skogestad, 2007) generates optimal variable combinations, c = u – Kx , which for the case with perfect state measurements are equivalent to the explicit MPC feedback laws, where K is the optimal state feedback matrix in a given region. More importantly, this link makes it possible to derive explicit feedback laws for cases with (1) state measurement error included and (2) measurement (rather than state) feedback. We further show how to generate optimal low-order controllers for unconstrained optimal control, also in the presence of noise.
One of the key problems in modelpredictivecontrol (MPC) is the inherent on-line computational complexity, which restricts its application to slow dynamic systems. To address this issue, multi-parametric programming ...
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One of the key problems in modelpredictivecontrol (MPC) is the inherent on-line computational complexity, which restricts its application to slow dynamic systems. To address this issue, multi-parametric programming technique is introduced in MPC (explicit MPC), where the optimization effort is moved off-line. The optimal solution is given in an explicitly piecewise affine function defined over a polyhedral subdivision of the set of feasible states. Instead of solving an optimization problem, the on-line work is simplified to identify the region the current state belongs to and simply evaluate the piecewise affine function. Hence, identifying of the member of the solution partition that contains a given point (referred to as a point location problem) impacts on the time to implement the explicitcontroller in real-time, which is one component of the complexity of explicit MPC. In this paper, two simple algorithms for point location problems are proposed to efficiently implement of explicit MPC solutions, which aim at reducing the number of polyhedral sets that are candidates to contain the state at the next time instant.
The present paper investigates the control of interleaved DC-DC converters. It proposes an alternative solution to balance the currents between the legs without using current transducer, relying instead on a feedback ...
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The present paper investigates the control of interleaved DC-DC converters. It proposes an alternative solution to balance the currents between the legs without using current transducer, relying instead on a feedback loop based on the measurement of the capacitor voltage ripple. The appropriate measurement circuit is proposed. The voltage control uses a modelpredictivecontrol scheme, which assumes the average model of a single leg converter, the unbalance being compensated separately. The controller intrinsically limits the current during transients, achieving protection of the semiconductor devices and avoiding coil saturation. The proposed control and balance methods are validated experimentally on a two-leg interleaved converter.
The present paper deals with the current control of a voltage source inverter connected to the grid through an LCL filter. It proposes model suitable for analysis and control that accounts for the switching behaviour ...
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The present paper deals with the current control of a voltage source inverter connected to the grid through an LCL filter. It proposes model suitable for analysis and control that accounts for the switching behaviour of the converter. Based on this improved model, a modelpredictivecontrol scheme is proposed, in order to provide a high bandwidth response, making it very suitable for applications such as active filtering. The control scheme is extended with an observer in order to reduce the number of required sensors and to eliminate noise. The effectiveness of the proposed scheme is demonstrated by experiments.
Parametric programming has received a lot of attention in the control literature in the past few years because modelpredictivecontrollers (MPC) can be posed in a parametric framework and hence pre-solved offline, re...
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Parametric programming has received a lot of attention in the control literature in the past few years because modelpredictivecontrollers (MPC) can be posed in a parametric framework and hence pre-solved offline, resulting in a significant decrease in on-line computation effort. In this paper we survey recent work on parametric linear programming (pLP) from the point of view of the control engineer. We identify three types of algorithms, two arising from standard convex hull paradigms and one from a geometric intuition, and classify all currently proposed methods tinder these headings. Through this classification, we identify a third standard convex hull approach that offers significant potential for approximation of pLPs for the purpose of control. We present the resulting algorithm, based on the beneath/beyond paradigm, that computes low-complexity approximate controllers that guarantee stability and feasibility.
Parametric programming has received a lot of attention in the control literature in the past few years because modelpredictivecontrollers (MPC) can be posed in a parametric framework and hence pre-solved offline, re...
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Parametric programming has received a lot of attention in the control literature in the past few years because modelpredictivecontrollers (MPC) can be posed in a parametric framework and hence pre-solved offline, resulting in a significant decrease in on-line computation effort. In this paper we survey recent work on parametric linear programming (pLP) from the point of view of the control engineer. We identify three types of algorithms, two arising from standard convex hull paradigms and one from a geometric intuition, and classify all currently proposed methods tinder these headings. Through this classification, we identify a third standard convex hull approach that offers significant potential for approximation of pLPs for the purpose of control. We present the resulting algorithm, based on the beneath/beyond paradigm, that computes low-complexity approximate controllers that guarantee stability and feasibility.
In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures;this wi...
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In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures;this will be referred to as the facet-to-facet property. It is shown by an example, whose solution is unique, that the facet-to-facet property does not hold in general. Consequently, some existing algorithms cannot guarantee that the entire parameter space will be explored. A simple modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Numerical results indicate that, compared to the original algorithms for parametric quadratic programs, the proposed method has lower computational complexity for problems whose solutions consist of a large number of critical regions. (c) 2006 Elsevier Ltd. All rights reserved.
A method which ensures uniqueness of the polyhedral partition of the parameter space for convex multiparametric quadratic programs (mp-QP) is presented. When the mp-QP has non-unique solutions, the norm of the solutio...
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ISBN:
(纸本)0780390989
A method which ensures uniqueness of the polyhedral partition of the parameter space for convex multiparametric quadratic programs (mp-QP) is presented. When the mp-QP has non-unique solutions, the norm of the solution vector is minimized and a unique affine optimizer function is identified for each region. It is proven, that under certain assumptions on the problem data, a globally continuous piecewise affine optimizer function is selected.
A modification of the geometric algorithm for solving multiparametric linear programs (mp-LP) is presented. The modification preserves the simplicity of the algorithm and ensures that the optimal, piecewise affine, ma...
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A modification of the geometric algorithm for solving multiparametric linear programs (mp-LP) is presented. The modification preserves the simplicity of the algorithm and ensures that the optimal, piecewise affine, mapping from parameter to solution space is continuous. When the mp-LP has non-unique solutions, the optimizer with the least Euclidian norm is selected.
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