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Embedded Model Predictive Control on Low-Cost Low-End Microcontroller for Motor Speed Control
Abstract
It is very well-known that the implementation of Model Predictive Controller (MPC) on embedded platforms is challenging due to computational complexities associated while solving an optimization problem. Although, there are many efficient embedded implementations existing by now, but for faster, more dynamic and non-linear control applications, no cost effective and memory efficient embedded solutions are present. In this paper, we show the implementation of embedded explicit MPC for a motor speed control application on a low-cost 8 bit PIC 18 series microcontroller from Microchip Technology. The offset-free explicit MPC is designed for reference tracking and constraints and disturbance handling. The developed control law is exported to low-level C code and utilized in hardware-in-the-loop co-simulations. We present the results of memory demand and control performance under various operating scenarios. The presented results show that the developed embedded MPC utilize about 40% of RAM and 92% of ROM for prediction horizon up to 3 samples. The performance of developed MPC is compared with the conventional PI controller. Overall results show that the presented approach is cost effective, portable, and gives better performance than the PI controller.
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This article presents an embedded active vibration suppression system featuring real-time explicit model predictive control (EMPC) that is implemented on a microcontroller unit (MCU). The EMPC controller minimizes the tip deflection of an aluminum cantilever beam driven by piezoceramic actuators, gaining its feedback from direct position measurements. The output and input performance of the EMPC method is compared to an analogously tuned positive position feedback (PPF) controller. An extensive analysis is provided on the cycle timing and memory needs of the explicit predictive vibration control scheme. The results demonstrate that the EMPC controller may achieve the same vibration suppression results compared to PPF with less input effort, while inherently respecting process constraints. Furthermore, we show that EMPC task execution timing is comparable in the random access memory (RAM) and read only memory (ROM) alternatives, suggesting that numerous current microcontrollers are suitable for EMPC-based active vibration control, in case the prediction model is kept simple.
Over the last decade, anesthesia research community witnessed numerous advances in controllers and their implementation platforms to control the depth of anesthesia (DoA) in a patient undergoing surgery. Today's operating theaters are extremely complex and crowded. New surgical techniques bring new medical technologies and more devices in the operation rooms, which often results in complex configurations, computer based control, and cable clutter. In an effort to reduce hardware size and to the improve quality control of anesthesia, we present a field programmable gate array (FPGA) based explicit model predictive control (EMPC) scheme which can take into account the control and state constraints that naturally arise in anesthesia. Real-time implementation of model predictive control (MPC), mainly requires solving an optimization problem at regular time intervals. We propose an FPGA-based MPC-on-a-chip algorithm with customized 32-bit floating-point addition, substation, and multiplication algorithms. Simulation results with four compart-mental Pk/PD model, input constraints and a variable bispectral index (BIS) set-point are presented. The real-time simulation results are achieved with Xilinx's Vertex 4 XC4VLX25-10FF668 FPGA.
Model Predictive Control (MPC) is an established con-trol technique in a wide range of process industries. The reason for this success is its ability to handle multivariable systems and systems having input, output or state constraints. Neverthless comparing to PID controller, the implementation of the MPC in miniaturized devices like Field Programmable Gate Arrays (FPGA) and microcon-trollers has historically been very small scale due to its complexity in implementation and its computation time requirement. At the same time, such embedded technologies have become an enabler for future manufacturing enterprisers as well as a transformer of organizations and markets. In this work, we take advantage of these recent advances in this area in the deployment of one of the most studied and applied control technique in the industrial engineering. In this paper, we propose an efficient firmware for the implementation of constrained MPC in the performed STM32 microcontroller using interior point method. Indeed, performances study shows good execution speed and low computational burden. These results encourage to develop predictive control algorithms to be programmed in industrial standard processes. The PID anti windup controller was also implemented in the STM32 in order to make a performance comparison with the MPC. The main features of the proposed constrained MPC framework are illustrated through two examples.
The Multi-Parametric Toolbox is a collection of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version 3.0 is a complete rewrite of the original toolbox with a more flexible structure that offers faster integration of new algorithms. The numerical side of the toolbox has been improved by adding interfaces to state of the art solvers and by incorporation of a new parametric solver that relies on solving linear-complementarity problems. The toolbox provides algorithms for design and implementation of real-time model predictive controllers that have been extensively tested.
For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton–Jacobi–Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.
Model predictive control algorithms achieve offset-free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled variables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems.
In past years, many advanced control strategies on numerous embedded platforms have been proposed and investigated to evaluate the effects of drugs dosing during closed loop control of anesthesia for a patient undergoing surgery. In today's era of automation, operating rooms are extremely complex and crowded, which often results in complex configurations, computer based control, and cable clutter. In this paper, we present a Field Programmable Gate Array (FPGA) based Explicit Model Predictive Control (EMPC) scheme to reduce the hardware size and to improve the quality control of anesthesia with simple configurations. We introduce an FPGA-based implementation of Binary Search Tree (BST) algorithm to evaluate a piecewise affine (PWA) control law, using customized 32-bit floating-point arithmetic. The FPGA-based EMPC strategy is tested for four-compartmental Pharmacokinetic-Pharmacodynamic (PK-PD) patient model to regulate the Bispectral Index (BIS) as a measure of Depth of Anesthesia (DoA) by controlling the drug infusion rate. The real-time simulation results for variable BIS set-point tracking are achieved with Xilinx's Vertex 4 XC4VLX25-10FF668 FPGA.
While model predictive control (MPC) is the industrially preferred method for advanced control in the process industries, it has not found much use in consumer products and safety-critical embedded systems applications in industries such as automotive, aerospace, medical, and robotics. The main barriers are implementability and dependability, where important factors are implementation of advanced numerical optimization algorithms on resource-limited embedded computing platforms and the associated complexity of verification. This challenge comes from a requirement of the use of ultrareliable hardware and software architectures in safety-critical applications, low-cost hardware in consumer products, or both. This paper surveys the state-of-the-art in the emerging field of dependable embedded MPC, and discusses some key challenges related to its design, implementation, and verification. A novel result is the study of a simulator-based performance monitoring and control selection method that monitors and predicts MPC performance and switches to a highly reliable backup controller in cases when the MPC experiences performance issues.
The book develops a systematic approach to motor drives. While the emphasis is on practice; extensive modeling, simulation and analysis is developed to assist readers in their understanding of the subject matter from fundamental principles. Also, each motor drive is illustrated with an industrial application in detail at the end of chapters to enable readers to relate theory to practice.
In this paper, an integrated hardware and software design method is developed to implement an MPC algorithm on an FPGA chip. This makes it possible to achieve the long-desired goal of extending MPC algorithms to field control so as to deal with constraints effectively. To expedite the numerical procedure of solving quadratic programming (QP) in the MPC algorithm, a QP solver based on embedded chips is designed to exploit the flexibility and efficiency of FPGA chips. With a carefully devised software architecture, a universal platform is proposed to be facilely deployed to field control applications. To demonstrate the efficacy, a prototype system is built based on a Xilinx FPGA chip. It is then applied to a motor servo tracking control system and achieves satisfactory control performance.
This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules,
and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer
variables. MLD systems include linear hybrid systems, finite state machines, some classes of discrete event systems, constrained
linear systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme
is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints,
and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer
variables, the resulting on-line optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP), for which efficient solvers have been recently developed. Some examples and a simulation case study on a complex
gas supply system are reported.
A real-time implementation of model predictive control (MPC) is presented in this paper. MPC, also known as receding horizon control and moving horizon control, is widely accepted as the controller of choice for multivariable systems that have inequality constraints on system states, inputs and outputs. For processes with slow dynamics and low sampling rates, MPC is typically implemented on a dedicated computer. For systems with fast dynamics such as those in MEMS, a hardware embedded MPC would be an appropriate controller implementation since the size and the application precludes the use of a dedicated computer. Recent manufacturing advances have opened the path for the fabrication of micromechanical devices and electronic subsystems under the same manufacturing and packaging process, thereby opening the path for the use of advanced control algorithms towards systems-on-chip applications.
This paper presents a hardware architecture for embedded real-time model predictive control (MPC). The computational cost of an MPC problem, which relies on the solution of an optimization problem at every time step, is dominated by operations on real matrices. In order to design an efficient and low-cost application-specific processor, we analyze the computational cost of MPC, and we propose a limited-resource host processor to be connected with an application-specific matrix coprocessor. The coprocessor uses a 16-b logarithmic number system arithmetic unit, which is designed using cotransformation, to carry out the required arithmetic operations. The proposed architecture is implemented by means of a hardware description language and then prototyped and emulated on a field-programmable gate array. Results on computation time and architecture area are presented and analyzed, and the functionality of the proposed architecture is verified using two case studies: a linear problem of a rotating antenna and a nonlinear glucose-regulation problem. The proposed MPC architecture yields a small-in-size and energy-efficient implementation that is capable of solving the aforementioned problems on the order of milliseconds, and we compare its performance and area requirements with other MPC designs that have appeared in the literature.
Efficient implementation of solvers for linear model predictive control on embedded devices
- G Frison
- D K M Kufoalor
- L Imsland
- J Bagterp
G. Frison, D. K. M. Kufoalor, L. Imsland, J. Bagterp et al., "Efficient
implementation of solvers for linear model predictive control on
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Design and verification of low-complexity explicit MPC controllers in MPT3
- M Kvasnica
- J Holaza
- B Takács
- D Ingole
M. Kvasnica, J. Holaza, B. Takács, and D. Ingole, "Design and
verification of low-complexity explicit MPC controllers in MPT3," in
Control Conference (ECC), 2015 European. IEEE, 2015, pp. 2595-2600.