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4: FPGA architectures, where arrays of logic blocks are surrounded by a ring of input/output blocks, connected together via interconnect.
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Model Predictive Control (MPC) feedback law is given by the solution to a multiparametric
Quadratic Programming (mp-QP) problem that can be pre-computed
off-line and stored in the form of Look-Up Table (LUT) to be used in on-line
synthesis. The on-line computation reduces to simple evaluations of a Piecewise
Affine (PWA) function, allowing implemen...
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Citations
... In general, polyhedral regions CRs are influenced by size of parameter vector and, more critically, by number of system constraints. These factors may lead number of regions to grow exponentially [36]. ...
In this paper, we propose a comparision of GPC and explicit GPC formulations to analyze performance of each algorithm in both offline optimization and online control stage. To demonstrate algorithms performance, we implemented a comparison between three simulated examples: a multivariable control of a Stirred Tank Reactor; an underactuated control of a Gantry Crane System; and multivariable control with transport delay of a Distillation Column. Our results show a reduction in the computational time of control action calculation, from 1.69 to 33 times, depending on the controller. Also, it is possible to significantly reduce memory requirement in explicit cases, depending on the formulation, due to reduced dimensionality.
... The form of unums used in their work is "Type II," which have many ideal mathematical properties but rely on LUTs for most operations. A key idea of unums is explained in detail in [8]. Type II unums are usually less amenable to fused operations. ...
... This procedure will be repeated until the very end of the binary tree structure (its last leaf). For the more details on SS and BST algorithm, see [8]. ...
... The fraction bits represent f , where 0 ≤ f < 1. Combining (7), (8), and (9), the posit bit string represents the value ...
In the explicit model predictive control (EMPC),
memory increases exponentially with the number of states,
inputs, constraints, and prediction horizons; this often limits its
applicability to large systems. In this article, we present a novel
memory reduction technique for the lightweight EMPC using a
novel posit number format implemented on a field-programmable
gate array (FPGA), aiming to reduce the memory footprints and
power utilization of the EMPC. We developed a fully automatic
framework for the design of fast embedded EMPC on FPGAs
using posit arithmetic and logical unit (ALU). The proposed
technique is based on encoding all data (i.e., the critical regions
and the feedback laws) as posit numbers, which can be viewed
as a more memory-efficient alternative to the IEEE 754 floatingpoint
standard. The performance and efficiency of the developed
posit-based offset-free EMPC are demonstrated on the anesthesia
control problem. We show the results of hardware-in-the-loop
co-simulation with the detailed analysis of the resource utilization,
power utilization, clock achieved, and the memory footprints
comparison between IEEE 754 floating-point and posit formats.
By doing so, we illustrate that the total memory footprints can
be reduced by 50%–75% with achieving low power utilization
as compared to floating-point numbers without sacrificing the
control performances. The proposed technique can be applied
on top of other existing complexity reduction techniques used in
EMPC as well as for the online optimization methods.
... Advance surgical techniques bring new biomedical technologies and more instrumentation in the ORs, which often results in complex configurations and big size machinery which occupies more space. Efforts have been made to improve the quality control and replace big size machines with embedded systems (see, [26]). ...
Model predictive control (MPC) has emerged as
an excellent control strategy owing to its ability to include
constraints in the control optimization and robustness to linear
as well as highly non-linear systems. There are many challenges
in real-time implementation of MPC on embedded devices,
including computational complexity, numerical instability, and
memory constraints. Advances in machine learning-based approaches
have widened the scope to replace the traditional and
intractable optimization algorithms with advanced algorithms.
In this paper, a novel deep learning-based model predictive
control (DNN-MPC) is presented. The proposed MPC uses recurrent
neural network (RNN) to accurately predict the future
output states based on the previous training data. Using deep
neural networks for the real-time embedded implementation
of MPC, on-line optimization is completely eliminated leaving
only the evaluation of some linear equations. Closed-loop
performance evaluation of the DNN-MPC is verified through
hardware-in-loop (HIL) co-simulation on ARM microcontroller
and a 4x speed-up in computational time for a single iteration is
achieved over the conventional MPC. Detailed analysis of DNNMPC
complexity (speed and memory requirement) is presented
and compared with traditional MPC. Results show that the
proposed DNN-MPC performs faster and with less memory
footprints while retaining the controller performance.
... On the downside, memory requirement for EMPC is high as compared to online MPC as all the possible cases of control problem needs to be identified and stored in the actual memory of embedded platform. Despite the associated memory demand, its distinguish features have extended its application to several areas of engineering, an overview of recent applications of EMPC can be found in [7,Chapter 3]. ...
It is well-known that the real-time implementation
of MPC is cumbersome because of the huge burden of solving
QP problem on-line at each sample time. Due to this, traditionally
MPC has been mainly restricted to processes with rather
slow dynamics, such as the ones encountered in the oil and
gas refineries. However, recent algorithmic advances (such as
the explicit MPC) allowed the application of MPC to problems
arising in the automotive or power electronics industry where
the time scales are in the milli- to microsecond range. This paper
focuses on the FPGA implementation of offset-free explicit
MPC and its detailed analysis for the position control of
PMDC motor. We show the analysis of controller computational
complexity in terms of memory, resource utilization, clock and
power consumption. Effect of various tuning parameters on
the number of regions is also presented with respect to the
changing prediction horizon length. Finally, the performance
of implemented offset-free explicit MPC is compared with the
standard explicit MPC and PI controller for reference-tracking,
constraints handling, and disturbance rejection. Results indicate
that the performance of offset-free explicit MPC is superior
but at the cost of increased memory footprint.
