2,235 research outputs found

    Robust explicit MPC design under finite precision arithmetic

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    We propose a design methodology for explicit Model Predictive Control (MPC) that guarantees hard constraint satisfaction in the presence of finite precision arithmetic errors. The implementation of complex digital control techniques, like MPC, is becoming increasingly adopted in embedded systems, where reduced precision computation techniques are embraced to achieve fast execution and low power consumption. However, in a low precision implementation, constraint satisfaction is not guaranteed if infinite precision is assumed during the algorithm design. To enforce constraint satisfaction under numerical errors, we use forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use this to inform the design of a constraint-tightening robust controller. Benchmarks with a classical control problem, namely an inverted pendulum, show how it is possible to guarantee, by design, constraint satisfaction for embedded systems featuring low precision, fixed-point computations

    Digital implementation of hierarchical piecewise-affine controllers

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    This paper proposes the design of hierarchical piecewise-affine (PWA) controllers to alleviate the processing time or prohibitive memory requirements of large controller structures. The constituent PWA modules of the hierarchical solution have fewer inputs and/or coarser partitions, so that they can reduce considerably the hardware resources required and/or the time response of the controller. A design methodology aided by CAD tools is employed to design the parameters of the controller, implement its architecture in an FPGA, and verify the static and dynamic behavior of the digital implementation by applying hardware-in-the-loop testing.Comunidad Europea FP7-IST-248858Ministerio de Ciencia e Innovación TEC2008-04920 y DPI2008-03847Junta de Andalucía P08-TIC-0367

    Circuit implementation of piecewise-affine functions based on lattice representation

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    This paper introduces a digital architecture to implement piecewise-affine (PWA) functions based on representation methods from the lattice theory. Given an explicit and continuous PWA function, the parameters required to implement the lattice approach can be obtained by an off-line preprocessing that can be automated. Other advantages of the proposal are that it implements a continuous PWA function with potentially no errors and the minimum number of parameters to store. This has been proven experimentally by implementing the proposal in a Xilinx FPGA and comparing its performance with other implementations, all of them addressing a typical non linear control problem.Comunidad Europea FP7-IST-248858Ministerio de Ciencia e Innovación TEC2008-04920 y DPI2008-03847Junta de Andalucía P08-TIC-0367

    Digital VLSI Implementation of Piecewise-Affine Controllers Based on Lattice Approach

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    This paper presents a small, fast, low-power consumption solution for piecewise-affine (PWA) controllers. To achieve this goal, a digital architecture for very-large-scale integration (VLSI) circuits is proposed. The implementation is based on the simplest lattice form, which eliminates the point location problem of other PWA representations and is able to provide continuous PWA controllers defined over generic partitions of the input domain. The architecture is parameterized in terms of number of inputs, outputs, signal resolution, and features of the controller to be generated. The design flows for field-programmable gate arrays and application-specific integrated circuits are detailed. Several application examples of explicit model predictive controllers (such as an adaptive cruise control and the control of a buck-boost dc-dc converter) are included to illustrate the performance of the VLSI solution obtained with the proposed lattice-based architecture

    Explicit Nonlinear Model Predictive Control of the Air Path of a Turbocharged Spark-Ignited Engine

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    International audiencePollutant emissions and fuel economy objectives have led car manufacturers to develop innovative and more sophisticated engine layouts. In order to reduce time-to-market and development costs, recent research has investigated the idea of a quasi-systematic engine control development approach. Model based approaches might not be the only possibility but they are clearly predetermined to considerably reduce test bench tuning work requirements. In this paper, we present the synthesis of a physics-based nonlinear model predictive control law especially designed for powertrain control. A binary search tree is used to ensure real-time implementation of the explicit form of the control law, computed by solving the associated multi-parametric nonlinear problem

    Explicit model predictive control accuracy analysis

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    Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of the partition. An actual implementation of this explicit MPC in low cost micro-controllers requires the data to be "quantized", i.e. represented with a small number of memory bits. An aggressive quantization decreases the number of bits and the controller manufacturing costs, and may increase the speed of the controller, but reduces accuracy of the control input computation. We derive upper bounds for the absolute error in the control depending on the number of quantization bits and system parameters. The bounds can be used to determine how many quantization bits are needed in order to guarantee a specific level of accuracy in the control input.Comment: 6 pages, 7 figures. Accepted to IEEE CDC 201

    Digital VLSI Implementation of Piecewise-Affine Controllers Based on Lattice Approach

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    This paper presents a small, fast, low-power consumption solution for piecewise-affine (PWA) controllers. To achieve this goal, a digital architecture for very-large-scale integration (VLSI) circuits is proposed. The implementation is based on the simplest lattice form, which eliminates the point location problem of other PWA representations and is able to provide continuous PWA controllers defined over generic partitions of the input domain. The architecture is parameterized in terms of number of inputs, outputs, signal resolution, and features of the controller to be generated. The design flows for field-programmable gate arrays and application-specific integrated circuits are detailed. Several application examples of explicit model predictive controllers (such as an adaptive cruise control and the control of a buck-boost dc-dc converter) are included to illustrate the performance of the VLSI solution obtained with the proposed lattice-based architecture.Peer reviewe

    A General Lattice Representation for Explicit Model Predictive Control

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