Embedded Model Predictive Control (MPC) using a FPGA

Model Predictive Control (MPC) is increasingly being proposed for application to miniaturized devices, fast and/or embedded systems. A major obstacle to this is its computation time requirement. Continuing our previous studies of implementing constrained MPC on Field Programmable Gate Arrays (FPGA), this paper begins to exploit the possibilities of parallel computation, with the aim of speeding up the MPC implementation. Simulation studies on a realistic example show that it is possible to implement constrained MPC on an FPGA chip with a 25MHz clock and achieve MPC implementation rates comparable to those achievable on a Pentium 3.0 GHz PC. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

Locally weighted learning model predictive control for nonlinear and time varying dynamics

This paper proposes an online learning control system that uses the strategy of Model Predictive Control (MPC) in a model based locally weighted learning framework. The new approach, named Locally Weighted Learning Model Predictive Control (LWL-MPC), is proposed as a solution to learn to control robotic systems with nonlinear and time varying dynamics. This paper demonstrates the capability of LWL-MPC to perform online learning while controlling the joint trajectories of a low cost, three degree of freedom elastic joint robot. The learning performance is investigated in both an initial learning phase, and when the system dynamics change due to a heavy object added to the tool point. The experiment on the real elastic joint robot is presented and LWL-MPC is shown to successfully learn to control the system with and without the object. The results highlight the capability of the learning control system to accommodate the lack of mechanical consistency and linearity in a low cost robot arm.

Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Low Effort L-i Nuclear Fusion Plasma Control Using Model Predictive Control Laws

One of the main problems of fusion energy is to achieve longer pulse duration by avoiding the premature reaction decay due to plasma instabilities. The control of the plasma inductance arises as an essential tool for the successful operation of tokamak fusion reactors in order to overcome stability issues as well as the new challenges specific to advanced scenarios operation. In this sense, given that advanced tokamaks will suffer from limited power available from noninductive current drive actuators, the transformer primary coil could assist in reducing the power requirements of the noninductive current drive sources needed for current profile control. Therefore, tokamak operation may benefit from advanced control laws beyond the traditionally used PID schemes by reducing instabilities while guaranteeing the tokamak integrity. In this paper, a novel model predictive control (MPC) scheme has been developed and successfully employed to optimize both current and internal inductance of the plasma, which influences the L-H transition timing, the density peaking, and pedestal pressure. Results show that the internal inductance and current profiles can be adequately controlled while maintaining the minimal control action required in tokamak operation.

Reservoir Management For Flood And Drought Protection Using Infinite Horizon Model Predictive Control

Model Predictive Control (MPC) is a control method that solves in real time an optimal control problem over a finite horizon. The finiteness of the horizon is both the reason of MPC's success and its main limitation. In operational water resources management, MPC has been in fact successfully employed for controlling systems with a relatively short memory, such as canals, where the horizon length is not an issue. For reservoirs, which have generally a longer memory, MPC applications are presently limited to short term management only. Short term reservoir management can be effectively used to deal with fast process, such as floods, but it is not capable of looking sufficiently ahead to handle long term issues, such as drought. To overcome this limitation, we propose an Infinite Horizon MPC (IH-MPC) solution that is particularly suitable for reservoir management. We propose to structure the input signal by use of orthogonal basis functions, therefore reducing the optimization argument to a finite number of variables, and making the control problem solvable in a reasonable time. We applied this solution for the management of the Manantali Reservoir. Manantali is a yearly reservoir located in Mali, on the Senegal river, affecting water systems of Mali, Senegal, and Mauritania. The long term horizon offered by IH-MPC is necessary to deal with the strongly seasonal climate of the region.

Modelling and predictive control techniques for building heating systems

Model predictive control (MPC) has often been referred to in literature as a potential method for more efficient control of building heating systems. Though a significant performance improvement can be achieved with an MPC strategy, the complexity introduced to the commissioning of the system is often prohibitive. Models are required which can capture the thermodynamic properties of the building with sufficient accuracy for meaningful predictions to be made. Furthermore, a large number of tuning weights may need to be determined to achieve a desired performance. For MPC to become a practicable alternative, these issues must be addressed. Acknowledging the impact of the external environment as well as the interaction of occupants on the thermal behaviour of the building, in this work, techniques have been developed for deriving building models from data in which large, unmeasured disturbances are present. A spatio-temporal filtering process was introduced to determine estimates of the disturbances from measured data, which were then incorporated with metaheuristic search techniques to derive high-order simulation models, capable of replicating the thermal dynamics of a building. While a high-order simulation model allowed for control strategies to be analysed and compared, low-order models were required for use within the MPC strategy itself. The disturbance estimation techniques were adapted for use with system-identification methods to derive such models. MPC formulations were then derived to enable a more straightforward commissioning process and implemented in a validated simulation platform. A prioritised-objective strategy was developed which allowed for the tuning parameters typically associated with an MPC cost function to be omitted from the formulation by separation of the conflicting requirements of comfort satisfaction and energy reduction within a lexicographic framework. The improved ability of the formulation to be set-up and reconfigured in faulted conditions was shown.

Constrained predictive control of ship fin stabilizers to prevent dynamic stall

In moderate to high sea states, the effectiveness of ship fin stabilizers can severely deteriorate due to nonlinear effects arising from unsteady hydrodynamic characteristics of the fins: dynamic stall. These nonlinear effects take the form of a hysteresis, and they become very significant when the effective angle of attack of the fins exceeds a certain threshold angle. Dynamic stall can result in a complete loss of control action depending on how much the fins exceed the threshold angle. When this is detected, it is common to reduce the gain of the controller that commands the fins. This approach is cautious and tends to reduce performance when the conditions leading to dynamic stall disappear. An alternative approach for preventing the effects while keeping high performance, consists of estimating the effective angle of attack and set a conservative constraint on it as part of the control objectives. In this paper, we investigate the latter approach, and propose the use of a model predictive control (MPC) to prevent the development of these nonlinear effects by considering constraints on both the mechanical angle of the fins and the effective angle of attack.

Power buffer with model predictive control for stability of vehicular power systems with constant power loads

Electrification of vehicular systems has gained increased momentum in recent years with particular attention to constant power loads (CPLs). Since a CPL potentially threatens system stability, stability analysis of hybrid electric vehicle with CPLs becomes necessary. A new power buffer configuration with battery is introduced to mitigate the effect of instability caused by CPLs. Model predictive control (MPC) is applied to regulate the power buffer to decouple source and load dynamics. Moreover, MPC provides an optimal tradeoff between modification of load impedance, variation of dc-link voltage and battery current ripples. This is particularly important during transients or starting of system faults, since battery response is not very fast. Optimal tradeoff becomes even more significant when considering low-cost power buffer without battery. This paper analyzes system models for both voltage swell and voltage dip faults. Furthermore, a dual mode MPC algorithm is implemented in real time offering improved stability. A comprehensive set of experimental results is included to verify the efficacy of the proposed power buffer.

Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

Predictive control using an FPGA with application to aircraft control

Alternative and more efficient computational methods can extend the applicability of model predictive control (MPC) to systems with tight real-time requirements. This paper presents a system-on-a-chip MPC system, implemented on a field-programmable gate array (FPGA), consisting of a sparse structure-exploiting primal dual interior point (PDIP) quadratic program (QP) solver for MPC reference tracking and a fast gradient QP solver for steady-state target calculation. A parallel reduced precision iterative solver is used to accelerate the solution of the set of linear equations forming the computational bottleneck of the PDIP algorithm. A numerical study of the effect of reducing the number of iterations highlights the effectiveness of the approach. The system is demonstrated with an FPGA-in-the-loop testbench controlling a nonlinear simulation of a large airliner. This paper considers many more manipulated inputs than any previous FPGA-based MPC implementation to date, yet the implementation comfortably fits into a midrange FPGA, and the controller compares well in terms of solution quality and latency to state-of-the-art QP solvers running on a standard PC. © 1993-2012 IEEE.

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.