Linear Model Predictive Control Strategy Research Articles

Non linear model predictive control strategy for the energy management of a P4 parallel hybrid electric vehicle

In this paper, the energy management strategies (EMS) as main fuel saving approaches are studied for a P4 parallel hybrid electric vehicle (HEV). The multiple power sources of the analysed HEV (one thermal engine and two electric motors) and the different vehicle driving conditions increase the complexity in designing an optimal EMS. To efficiently solve the fuel minimization problem, a non linear Model Predictive Control (NL-MPC) is proposed as energy optimization strategy of the examined HEV. First, a vehicle simulation model is developed in Matlab/Simulink environment. A NL-MPC-controller is designed, implemented into the adopted code and coupled to the vehicle model. The effectiveness of developed NL-MPC approach is evaluated in two different driving cycles, also including various initial battery State of Charge. A comparison with a well-recognized real-time EMS strategy, namely heuristic/rule based (RB) approach, is performed over WLTC and a Real Driving Cycle (RDC). The numerical outcomes demonstrate the capability of NL-MPC controller at significantly improving the fuel consumption with respect to the RB strategy (maximum advantage of 9% and 15% over WLTC and RDC), thus providing an excellent and robust method in the HEV powertrain control with satisfactory performance.

Model Predictive Control Strategies for Turbine Electrified Energy Management

Abstract The increasing electrification of aircraft propulsion systems is leading to new control architectures being developed to address integration between electric machines and gas-based turbine engines. For hybrid-electric propulsion systems, current conceptual architectures often couple electric machines with the shafts of gas turbine engines and introduce energy storage. Leveraging the electrical power system of hybridized engines, Turbine Electrified Energy Management (TEEM) is a recent control approach that improves transient operability in an effort to enable more efficient and lighter weight turbomachinery. This study seeks to expand TEEM's application beyond traditional proportional-integral (PI) control by presenting linear model predictive control (MPC) schemes to execute the TEEM concept. Through constraint selection and cost function design, transient operability goals for TEEM are considered with no external logic or saturation. Unique to the designs are the use of a washout filter, which simplifies transient detection and motor activation logic. The proposed architectures are implemented with both centralized MPC and distributed MPC approaches, and comparisons are drawn to a benchmark PI controller simulated on a nonlinear turbofan engine model at one ground condition and one cruise condition. Performance is evaluated using compressor maps, stall margin performance, and two novel metrics: transient stack usage and transient excursion integral. Results reveal the linear MPC scheme performs comparably to the baseline controller and can be implemented in at least two distinct configurations with potential for further modifications, thus establishing the groundwork for future investigations.

Evaluation of two model predictive control schemes with different error compensation strategies for power management in fuel cell hybrid electric buses

Fuel cell hybrid electric buses (FCHEBs) employing hydrogen fuel cells as the main power source and supercapacitors as the energy buffer could be a feasible electrified transportation technology. This paper evaluates two model predictive control (MPC) schemes with different error compensation strategies for power management in FCHEBs: MPC scheme with Adaptive Compensation (denoted as AC-MPC) and MPC scheme with Gaussian Process Regression Compensation (denoted as GPRC-MPC). AC-MPC introduces adaptive weights based on the supercapacitor state of charge (SOC) and compensates for the errors associated with the linearization of the nonlinear fuel cell/supercapacitor hybrid energy storage system. GPRC-MPC utilizes Gaussian process regression to predict and compensate for the load disturbance error and the residual error. AC-MPC and GPRC-MPC are evaluated using the New York Bus (NYBus) drive cycle and a drive cycle collected along the GBG17 bus route in Sweden. Simulation results demonstrate the effectiveness of AC-MPC and GPRC-MPC in improving the hydrogen system performance by reducing the hydrogen consumption and the maximum fuel cell current change rate compared to the linear MPC scheme without any compensation while ensuring that the supercapacitor SOC is bounded.

An intelligent control approach for defect-free friction stir welding

An intelligent control approach is proposed as an alternative for the friction stir welding of an aluminum alloy. A validated empirical model is re-written from transfer functions to a set of ordinary differential equations, allowing to observe the force dynamics as a function of inputs of interest. A defect-free set-point is proposed for exploiting available labeled experimental data which defines operational boundaries and a region in which the probability of achieving defect-free welds with good mechanical properties is the highest. An intelligent controller in the fashion of a recurrent neural network is constructed. Computational experiments were carried out to verify the adequacy in disturbance rejection as well as to visualize the capabilities in achieving the proposed defect-free set-point by the controller. The intelligent approach is compared with a set of decoupled proportional-integral controllers and a linear model predictive control strategy. From this study, it is concluded that the intelligent controller shows superiority and good applicability for the studied problem.

Physics-based linear model predictive control strategy for three-way catalyst air/fuel ratio control

The Current practice of air-fuel ratio control relies on empirical models and traditional PID controllers, which require extensive calibration to maintain the post-catalyst air-fuel ratio close to stoichiometry. In contrast, this work utilizes a physics-based Three-Way Catalyst (TWC) model to develop a model predictive control (MPC) strategy for air-fuel ratio control based on internal TWC oxygen storage dynamics. In this paper, parameters of the physics-based temperature and oxygen storage models of the TWC are identified using vehicle test data for a catalyst aged to 150,000 miles. A linearized oxygen storage model is then developed from the identified nonlinear model, which is shown via simulation to follow the nonlinear model with minimal error during nominal operation. This motivates the development of a Linear MPC (LMPC) framework using the linearized TWC oxygen storage model, reducing the requisite computational effort relative to a nonlinear MPC strategy. In this work, the LMPC utilizing a linearized physics-based TWC model is proven suitable for tracking a desired oxygen storage level by controlling the commanded engine air-fuel ratio, which is also a novel contribution. The offline simulation results show successful tracking performance of the developed LMPC framework.

Joint Route Guidance and Demand Management for Real-Time Control of Multi-Regional Traffic Networks

In this work, we propose a joint route guidance and demand management strategy for multi-region networks with macroscopic traffic dynamics. Route guidance is used to identify the optimal transfer flows between neighbouring regions so that the trip completion rate across all regions is maximized. Demand management is utilized to control the traffic flows entering the network by forcing a portion of the traffic flows to wait at their origin. Towards this direction, we develop a Model Predictive Control (MPC) framework that aims to minimize the total time spent by all vehicles in the network (including the waiting time at the origin) by jointly optimizing the demand flows allowed in the network and the transfer flows between regions. To solve the resulting nonconvex and nonlinear optimization problem, by relaxing the nonconvex constraints, we develop a novel Linear Programming formulation that provides tight lower bounds on the optimal solution, as well as a feasible solution through the proposed MPC framework. Furthermore, (in another formulation) we restrict each region to only operate in the free-flow regime of the macroscopic fundamental diagram, which enables the transformation of the problem to a linear MPC formulation which can be solved in real-time using standard solvers and which provides a feasible solution to the original MPC problem. Extensive simulation results demonstrate that the linear MPC schemes execute in real-time and yield near-optimal results even under heavy traffic scenarios.

Linear model predictive control for the reduction of auxiliary electric heating in residential self-assisted ground-source heat pump systems

This article presents a linear model predictive control strategy for the operation of a “self-assisted” ground-source heat pump (GSHP) to reduce auxiliary electric heating in residential applications equipped with undersized boreholes. The self-assisted configuration uses an electric heating element at the heat-pump outlet to inject heat into the bore field when approaching peak power demand. A linear control-oriented model is proposed to account for both the source-side and load-side GSHP dynamics. The ground heat transfer is predicted using the bore field’s ground-to-fluid thermal response factor, thus allowing for any bore field configuration while accounting for thermal capacity effects. Real historic ambient temperature forecasts and their corresponding historic recorded ambient temperatures from Montreal are used in this article. The coefficient of performance (COP) nonlinearity is circumvented with an iterative approach. A Kalman filter is used to dynamically adjust the bias on the predicted returning fluid temperature. On a borehole undersized by 15%, the control strategy reduces auxiliary electric heating by 96% over 20 years at the cost of a 5.53% increase in total energy consumption. Due to the occasional simultaneous heat injection and auxiliary heating, the yearly peak power demand is increased.

Model Predictive Control with Adaptive Strategy Applied to an Electric Submersible Pump in a Subsea Environment

An automatic control of Electric Submersible Pumps (ESPs), employed for artificial lift oil production, is desired in order to ensure safe operation while satisfying pump and well constraints. In this context, the use of an advanced control strategy, such as model predictive control (MPC), can be beneficial in order to deal with the process constraints, variables coupling and optimal operation. In this paper, a linear MPC strategy was applied to an ESP model in order to keep the pump inlet pressure in a desired reference value, minimizing the pump power and respecting the variables constraints. Model adaptation based on homotopic transition between models was proposed for plant nonlinear response regions broadening the range of control.

Gain Scheduling Model Predictive Control of the New TCP-100 Parabolic Trough Field

Advanced control strategies can play an important role in improving the efficiency of solar plants. In particular, linear model predictive control strategies have been applied successfully when controlling solar trough plants. However, if the control algorithm uses a linear model associated only to one operating point, when the plant is working far from the design conditions, the performance of the controller may deteriorate.In this paper, a gain scheduling model predictive control strategy is designed for the new PTC TCP-100 research facility at the PSA, currently under construction, is presented. Simulation results are provided using a mathematical model of the solar field, showing the good performance of the proposed strategy.

Adaptive heat pump and battery storage demand side energy management

An adaptive linear model predictive control strategy is introduced for the problem of demand side energy management, involving a photovoltaic device, a battery, and a heat pump. Moreover, the heating influence of solar radiation via the glass house effect is considered. Global sunlight radiation intensity and the outside temperature are updated by weather forecast data. The identification is carried out after adapting to a time frame witch sufficiently homogeneous weather. In this way, in spite of the linearity an increase in precision and cost reduction of up to 46% is achieved. It is validated for an open and closed loop version of the MPC problem using real data of the ambient temperature and the global radiation.

An Efficient Inexact NMPC Scheme with Stability and Feasibility Guarantees

Abstract: In this paper, an inexact nonlinear model predictive control scheme with reduced computational complexity is proposed. The presented approach exploits fixed sensitivity information precomputed offline at a reference value. This allows one to avoid the online computational effort resulting from the propagation of sensitivities and possibly the corresponding condensing routine when solving the optimal control problem with a sequential quadratic programming method. By performing a numerical simulation of the nonlinear dynamics online, feasibility of the closed-loop trajectories can be preserved in contrast to linear model predictive control schemes. Nominal stability guarantees of the approach are derived and the effectiveness of the scheme is demonstrated on a non-trivial example.

Predictive control for embedded systems

Recent years have seen a drive to gain the theoretical guarantees and proven practical benefits of model predictive control (MPC) in a broad range of new application areas. The underlying theory of MPC has become well-established over the last decade, and it is now a simple and powerful paradigm for implementing complex control laws. MPC is currently the only technique available for synthesizing controllers that can explicitly ensure constraint satisfaction by design and easily allows for the incorporation of nonlinear dynamics. Contrary to the classic application areas of MPC involving expensive products, slow sampling rates, and massively complex plants, these new systems are characterized by their aggressive demand for fast sample rates, high reliability, low cost, and/or efficient use of energy. This special issue contains seven papers addressing new control and optimization methods, as well as computational software, for implementing predictive control on embedded platforms for high-speed dynamical systems. Hartley et al. 1 presents a field programmable gate array (FPGA)-based model predictive controller (MPC) for two phases of spacecraft rendezvous. The developed interior-point solver is accelerated by moving the main computational component, solving a system of linear equations, onto FPGA hardware. The measured timing indicates a substantial acceleration in computational time. Herceg et al. 2 presents a review of common active set algorithms that have been deployed for the implementation of fast MPC. The extensive theoretical and simulation-based analysis suggests directions for improvements specific to MPC computation. Liniger et al. 3 develops a nonlinear receding horizon-based controller for the racing of small (1:43 scale) RC cars. The nonlinear optimization problems are linearized at each time step and the resulting quadratic programs (QPs) are solved in embedded hardware in milliseconds, resulting in a 50 Hz sampling rate with cars traveling more than 3 m/s. Necoara et al. 4 presents a novel linear model predictive control scheme for use with quadratic programing software that may return a suboptimal or even infeasible solution. The scheme uses an estimate of infeasibility and suboptimality to adaptively tighten constraints and, thereby, ensures recursive satisfaction of constraints and asymptotic stability of the closed-loop system. Holaza et al. 5 develops a novel technique for synthesizing reduced complexity explicit MPC laws, which provide closed-loop stability and recursive satisfaction of constraints. The process involves the automatic generation of a simpler control law over a reduced partition via the solution of a convex optimization problem. Quirynen et al. 6 presents a tutorial of online optimization algorithms and efficient code implementations for embedded nonlinear model predictive control. The ACADO Toolkit for MATLAB is used to explain and showcase how these methods can solve practically relevant problems in only a few tens of microseconds. Kufoalor et al. 7 demonstrates how an existing PC-based industrial MPC solution can be migrated to an embedded platform. The real-time considerations necessary to achieve a functional high-performance predictive controller on a low-cost embedded hardware, with limited computational resources are detailed. We thank the editors of Optimal Control Applications and Methods for hosting this special issue, especially Martin Wells for his invaluable help and guidance.

Input-to-state stability properties of relaxed barrier function based MPC

We analyze robust stability properties of linear model predictive control schemes that are based on relaxed logarithmic barrier functions. It is shown that the corresponding closedloop system is globally exponentially stable in the nominal case as well as input-to-state stable with respect to arbitrary additive disturbances. Possible benefits and the practical relevance of the presented approach are discussed and illustrated by means of a numerical example.

Model Predictive Control in Pulsed Electrochemical Machining

In this work a Model Predictive Control (MPC) approach is used for controlling a Pulsed Electrochemical Machining (PECM) process. The MPC problem is formulated in order to optimally reach a desired state while satisfying various restrictions. PECM is modeled as a constrained nonlinear system. In the first approach the system is input-output linearized and a linear MPC scheme is applied to control it. In comparison a second approach uses the linearization around the current working point resulting in a Linear Time Variant system. This linear system is controlled using Linear Time Variant MPC (LTV-MPC). The simulation results are compared and the most promising controller is implemented on a real time platform controlling a PECM plant. The experimental results with online parameter estimation are shown and discussed.

A Reduced Dantzig-Wolfe Decomposition for a Suboptimal Linear MPC

Linear Model Predictive Control (MPC) is an efficient control technique that repeatedly solves online constrained linear programs. In this work we propose an economic linear MPC strategy for operation of energy systems consisting of multiple and independent power units. These systems cooperate to meet the supply of power demand by minimizing production costs. The control problem can be formulated as a linear program with block-angular structure. To speed-up the solution of the optimization control problem, we propose a reduced Dantzig-Wolfe decomposition. This decomposition algorithm computes a suboptimal solution to the economic linear MPC control problem and guarantees feasibility and stability. Finally, six scenarios are performed to show the decrease in computation time in comparison with the classic Dantzig-Wolfe algorithm.

Cooperative distributed MPC for tracking

AbstractThe problem of controlling large scale systems, usually divided into subsystems controlled by different agents, is usually solved using cooperative distributed control schemes, where the agents share open-loop information in order to improve closed-loop performance, (Rawlings and Mayne 2009, Chapter 6). In this paper we proposed a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems, which is able to steer the system to any admissible set point in an admissible way. Feasibility is ensured under any changing of the target steady state. The proposed controller is applied to a four tanks system.

Cooperative distributed model predictive control

In this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition. The control strategy has the following features: hard input constraints are satisfied; terminating the iteration of the distributed controllers prior to convergence retains closed-loop stability; in the limit of iterating to convergence, the control feedback is plantwide Pareto optimal and equivalent to the centralized control solution; no coordination layer is employed. We provide guidance in how to partition the subsystems within the plant. We first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class. We also establish that under perturbation from a stable state estimator, the origin remains exponentially stable. For plants with sparsely coupled input constraints, we provide an extension in which the decision variable space of each suboptimization is augmented to achieve Pareto optimality. We conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies.

Methodology for Designing and Comparing Robust Linear versus Gain-Scheduled Model Predictive Controllers

A methodology is proposed to design a robust Gain-Scheduled Model Predictive Control (MPC) strategy and to quantify the relative advantages of this controller versus a Linear MPC strategy. For the purpose of analysis and controller design, the process is represented by a nonlinear state-affine model identified from input−output data. This model can be split in linear and nonlinear terms where the linear part is used for controller design and the nonlinear part is accounted for as model uncertainty. Then, robust stability and robust performance tests are formulated based on linear matrix inequalities where the manipulated variables weight of the controllers is tuned to maximize performance. The uncertainty bounds used for the robustness tests are obtained in an iterative fashion by using the frequency response of the manipulated variable with respect to the feedback error. The control strategy performance is quantified by the ratio between the error norm and the disturbance norm. Finally, a case study involving a multiple-input−multiple-output bioreactor is presented. The study is able to predict for which range of operation the Gain-Scheduling MPC surpasses the performance of the Linear MPC.

Nonlinear Model Predictive Control of Cement Grinding Circuits

Based on a reduced-order model of a cement grinding circuit, a non linear model predictive control strategy is developed. The first step of this NMPC study is the definition of control objectives which consider product fineness, product flow rate and/or grinding efficiency. At this stage, one of the main concerns is to relate these objectives to easily measurahle particle weight fractions. Second, NMPC is implemented so as to take the various constraints on the manipulated variables and operating conditions of the mill into account. Third, robustness with respect to model uncertainties is analyzed, and the most critical parameters are highlighted. Finally, an NMPC scheme, combining a stable inner loop for controlling the mill flow rate and a DMC-like compensation of the model mismatch, is proposed.

Application of Wiener model predictive control (WMPC) to a pH neutralization experiment

pH control is recognized as an industrially important, yet notoriously difficult control problem. Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are considered to be ideal for representing this and several other nonlinear processes. Wiener models require little more effort in development than a standard linear step-response model, yet offer superior characterization of systems with highly nonlinear gains. These models may be incorporated into model predictive control (MPC) schemes in a unique way which effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC. In this paper, Wiener model predictive control (WMPC) is evaluated experimentally, and also compared with benchmark proportional integral derivative (PID) and linear MPC strategies, considering the effects of output constraints and modeling error.