Robust Model Predictive Control Controller Research Articles

Lane-changing control for hybrid electric vehicles with dedicated hybrid transmission based on robust model predictive control

Car-following and lane-changing are extremely important for vehicles. The traditional adaptive cruise control (ACC) strategy has various drawbacks due to the complicated driving conditions. A new control strategy of robust model predictive control (RMPC) for car-following and lane-changing is proposed based on a new type of hybrid electric vehicle (HEV) with dedicated hybrid transmission (DHT-HEV). The control model includes a vehicle model, a following and lane-changing model and an RMPC controller. The vehicle model integrates the DHT-HEV and dynamic models with a longitudinal dynamic model, seven degrees of freedom (DOF) vehicle dynamic model and three DOF control model. The following and lane-changing model is described as car-following and lane-changing models of two-quintic function. The RMPC controller is used to balance the control of vehicle longitudinal and lateral dynamics with the lateral acceleration disturbance. Simulation results demonstrate that the RMPC controller can track the reference trajectory during two lane-changing process when the test scenarios of different accelerations are set compared with the conventional ACC control. Different Np (predictive horizon) and Nc (control horizon) are also analysed to improve the solving performance of RMPC. Results indicate that the solving performance of the system is optimal when Np = 30 and Nc = 1. Furthermore, different weight coefficient matrixes ( Q and R) are taken into the consideration by coordinating the car-following performance and lateral stability. Accordingly, the controllers of RMPC-LC, RMPC-ACC and RMPC-LA are set, demonstrating that the control of RMPC-LA best balances two aspects and is always within a safe car-following distance. Meanwhile, the hardware in the loop (HIL) is utilised to verify the effectiveness of the proposed RMPC control strategy, which comprises model compilation, the establishment connection between the D2P ECU and the simulator and control input.

Platoon-centered control for eco-driving at signalized intersection built upon hybrid MPC system, online learning and distributed optimization part II: Theoretical analysis

Extensive studies developed eco-driving strategies to smooth traffic and reduce energy consumption and emission at signalized intersections. Part I (Zhang and Du, 2022) of this study developed a novel platoon-centered control for eco-driving (PCC-eDriving), considering a mixed flow involving Connected and Autonomous Vehicles (CAVs) and Human-Driven Vehicles (HDVs). This PCC-eDriving is mathematically implemented by a hybrid Model Predictive Control (MPC) system and solved by an active-set based optimal condition decomposition algorithm (AS-OCD). It generates discrete control laws for a platoon to approach, split as sub-platoons as needed, and then pass the intersections smoothly and efficiently. Though the numerical experiments validated the effectiveness, the theoretical properties of the hybrid MPC system and the solution algorithms were not investigated. Part II of this study thus focused on these theoretical analyses. Mainly, we first analyzed and proved the MPC sequential feasibility and hybrid system switching feasibility to guarantee the control continuity of the hybrid MPC system. Next, we factored CAV control uncertainties and proved the Input-to-state stability of the robust MPC controller. These proofs theoretically ensured the effectiveness and robustness of the hybrid MPC system. Last, we proved the solution optimality and convergence of the AS-OCD algorithm. It confirmed that the AS-OCD algorithm could find the global optimal solutions for the MPC optimizers with a linear convergence rate.

Offline Computation of the Explicit Robust Model Predictive Control Law Based on Deep Neural Networks

A significant challenge in robust model predictive control (MPC) is the online computational complexity. This paper proposes a learning-based approach to accelerate online calculations by combining recent advances in deep learning with robust MPC. The use of soft constraint variables addresses feasibility issues in the robust MPC design, while the employment of a symmetrical structure deep neural network (DNN) approximates the robust MPC control law. The symmetry of the network structure facilitates the training process. The use of soft constraints expands the feasible region and also increases the complexity of the training data, making the network difficult to train. To overcome this issue, a dataset construction method is employed. The performance of the proposed method is demonstrated through simulated examples, and the proposed algorithm can be applied to control systems in various fields such as aerospace, three-dimensional printing, optical imaging, and chemical production.

Neural-Network-Based Adaptive Model Predictive Control for a Flexure-Based Roll-to-Roll Contact Printing System

High-precision contact force control is essential for continuous roll-to-roll contact printing via mechanical contact on flexible web substrates using stamps. Nonuniformly controlled stamp contact force will cause failures during printing, especially for large-area printing processes. Due to their high precision in positioning and force control, flexure mechanisms have been applied in roll-to-roll contact printing systems; however, conventional physical model-based control systems cannot manage the nonlinear effects that exist in flexure-based roll-to-roll contact printing systems. To achieve precise contact force control, we propose a neural-network-based adaptive model predictive control for a flexure-based roll-to-roll contact printing system. The nonlinearity of the flexure mechanism is learned and modeled by an artificial neural network. To eliminate the steady-state error caused by model mismatches and external disturbances, an online adaptive mechanism is designed via updating the biases of the output layer of the neural network model. Experimental results show that the root-mean-square error of the contact force can be controlled in the range of 0–0.075 N with balances on two ends of the print roller, outperforming a proportional–integral–derivative controller, a neural-network-based standard model predictive control (MPC) controller, and a neural-network-based robust MPC controller. The proposed control algorithm is implemented in a microcontact printing process that prints 45- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m width gold patterns and achieves a variation of 0.3 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m in the average gold line width at different locations on an 88.9-mm width flexible substrate. The uniform microscale printing results have shown the effectiveness of the proposed neural-network-based adaptive model predictive control in the applied printing process.

Research on Robust Model Predictive Control Strategy of Wind Turbines to Reduce Wind Power Fluctuation

• Establish a robust model predictive control (RMPC) strategy for wind turbines based on wind speed uncertainty. • The error model of the nominal system and actual system is constructed and Lyapunov stability is used to prove that the error system tends to be stable. • Simulation analysis of the influence of RMPC strategy on wind turbine operation at different stable operating points. In the process of wind power generation, the random fluctuation of wind speed affects the smooth operation of the wind turbine and the stability of the output power of the wind turbine. Aiming at the influence of wind speed random fluctuation on the stable operation of wind turbines, this paper regards wind speed random fluctuation as bounded disturbance and adopts Robust Model Predictive Control (RMPC) strategy to divide the actual wind power system with wind speed disturbance into two parts: undisturbed nominal system and perturbed parts. As for the mismatch between the actual wind power system and the nominal system, the state of the actual wind power system is limited to a constant set by a certain feedback control law. The feedback control law and robust invariant set are then solved off-line via linear matrix inequalities (LMI). The 5MW wind turbine model developed by Nrel is used to simulate the feasibility of the algorithm on the MATLAB platform. RMPC control strategy can achieve the control goals of maximum wind energy capture at low wind speed and constant power operation at high wind speed. RMPC can effectively reduce the influence of wind speed uncertainty on stable operation of wind turbines, reduce output power fluctuation and improve power generation quality.

Path tracking control strategy for off-road 4WS4WD vehicle based on robust model predictive control

With the increasing requirements for vehicle adaptability and maneuverability in various road environments, four-wheel-steering four-wheel-drive (4WS4WD) vehicles have attracted wider attention. This paper presents a robust model predictive control-based strategy for the path tracking of 4WS4WD vehicles considering external disturbances. The strategy combines model predictive control (MPC) and control allocation under an upper–lower structure. The main objective of the present work is to improve the robustness and stability of path tracking by developing an MPC algorithm in the upper layer. The controller design considers general disturbances caused by allocation errors and sudden disturbances caused by an outer force in the offset model. Based on the offset model, a robust MPC control law is obtained by converting the robustness constraints into a linear matrix inequality. The control law is mathematically demonstrated to be stable in multidisturbed conditions via the Lyapunov stability theorem. Through comparison with a similar control algorithm of path tracking and applying it on different uneven ground conditions, the proposed robust algorithm is found to effectively overcome disturbances on the system.

Dynamic Lane Tracking Control of the Commercial Vehicle Based on RMPC Algorithm Considering the State of Preceding Vehicle

In order to improve the adaptability of the lane keeping control system to complex environments, a dynamic lane tracking control strategy of the commercial vehicle based on the robust model predictive control (RMPC) algorithm is proposed considering the state of the preceding vehicle. An RMPC controller is designed with path deviation and control increment as the objective function. The model predictive control problem is transformed into a min–max optimization problem. The linear matrix inequality (LMI) is used for the optimal solution to obtain the optimal control quantity. The strategy to improve the safety and comfort dynamically in the process of lane keeping is designed by adjusting the weight coefficient matrix of RMPC based on fuzzy theory. The results of the simulation and HiL test show that the RMPC controller can meet the requirement of adjusting the lane tracking process dynamically according to the state of the preceding vehicle, which keeps the balance between safety and comfort.

Robust MPC for Systems With Model Uncertainties and Measurement Outliers

This paper considers the observer-based output feedback robust model predictive control (RMPC) problem for systems with model uncertainties and possible measurement outliers. For the sake of alleviating the effects from possible abnormal measurements, we design a set of observer-based output feedback RMPC controllers with the saturation constraint where the saturation level is adaptive according to the estimation errors. The purpose of the addressed problem is to design a set of desired RMPC controllers so as to guarantee the robustness and the asymptotical stability of the closed-loop system. Sufficient stability conditions are obtained by solving a time-varying terminal constraint set of an auxiliary optimization problem, and the corresponding control law and the upper bound of the quadratic cost function are derived. In addition, an algorithm including both off-line and on-line parts is provided to find a sub-optimal solution. Finally, two simulation examples are employed to illustrate the effectiveness of the proposed RMPC approach.

Robust model predictive control for multirate systems with model uncertainties and circular scheduling

SummaryIn this article, the robust model predictive control (RMPC) problem on the basis of output feedback (OF) is dealt with for a class of multirate time‐varying systems with polyhedral uncertainties and limited‐bandwidth channels. For alleviating the communication burden caused by the limited transmission capacity, the Round‐Robin (RR) protocol is exploited to allocate transmission permissions in a pre‐scheduled order. Meanwhile, in order to reduce the communication cost while ensuring the system performance, the multirate mechanism is presented to govern the update rate of the plant and the sampling rate of the sensors. By means of the lifting technique, given a uniform sampling rate, a comprehensive augmentation system is established on the fixed moving horizon. The objective of the addressed RMPC problem is to design a set of OF‐based RMPC controllers such that, in the presence of the multirate scheme and the RR transmission protocol, the desirable performance is guaranteed. Then, the desired RMPC gains are directly obtained, with the help of inequality analysis technique and RR‐dependent Lyapunov‐like approach, to ensure the asymptotic convergence of system states. Two illustrative examples are given, which include a DC motor system and a numerical simulation example, to demonstrate the effectiveness of the proposed protocol‐based RMPC controller design strategy.

Robust Linear Control of Boost and Buck-Boost DC-DC Converters in Micro-Grids with Constant Power Loads

Power distribution systems nowadays are highly penetrated by renewable energy sources, and this explains the dominant role of power electronic converters in their operation. However, the presence of multiple power electronic conversion units gives rise to the so-called phenomenon of Constant Power Loads (CPLs), which poses a serious stability challenge in the overall operation of a DC micro-grid. This article addresses the problem of enhancing the stability margin of boost and buck-boost DC-DC converters employed in DC micro-grids under uncertain mixed load conditions. This is done with a recently proposed methodology that relies on a two-degree-of-freedom (2-DOF) controller, comprised by a voltage-mode Proportional Integral Derivative (PID) (Type-III) primary controller and a reference governor (RG) secondary controller. This complementary scheme adjusts the imposed voltage reference dynamically and is designed in an optimal fashion via the Model Predictive Control (MPC) methodology based on a specialized composite (current and power) estimator. The outcome is a robust linear MPC controller in an explicit form that is shown to possess interesting robustness properties in a wide operating range and under various disturbances and mixed load conditions. The robustness and performance of the proposed controller/observer pair under steady-state, line, and mixed load variations is validated through extensive Matlab/Simulink simulations.

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

Hierarchical Energy Management System for Microgrid Operation Based on Robust Model Predictive Control

This paper presents a two-level hierarchical energy management system (EMS) for microgrid operation that is based on a robust model predictive control (MPC) strategy. This EMS focuses on minimizing the cost of the energy drawn from the main grid and increasing self-consumption of local renewable energy resources, and brings benefits to the users of the microgrid as well as the distribution network operator (DNO). The higher level of the EMS comprises a robust MPC controller which optimizes energy usage and defines a power reference that is tracked by the lower-level real-time controller. The proposed EMS addresses the uncertainty of the predictions of the generation and end-user consumption profiles with the use of the robust MPC controller, which considers the optimization over a control policy where the uncertainty of the power predictions can be compensated either by the battery or main grid power consumption. Simulation results using data from a real urban community showed that when compared with an equivalent (non-robust) deterministic EMS (i.e., an EMS based on the same MPC formulation, but without the uncertainty handling), the proposed EMS based on robust MPC achieved reduced energy costs and obtained a more uniform grid power consumption, safer battery operation, and reduced peak loads.

Switching Tube-Based MPC: Characterization of Minimum Dwell-Time for Feasible and Robustly Stable Switching

We study the problem of characterizing mode dependent dwell-times that guarantee safe and stable operation of disturbed switching linear systems in a model predictive control (MPC) framework. We assume the switching instances are not known a priori , but instantly at the moment of switching. We first characterize dwell-times that ensure feasible and stable switching between independently designed robust MPC controllers by means of the well established exponential stability result available in the MPC literature. Then, we employ the concept of multiset invariance to improve on our previous results, and obtain an exponential stability guarantee for the switching closed-loop dynamics. The theoretical findings are illustrated via a numerical example.

Robustness Study of a Cascaded Dual Model-Predictive Control Applied to Synchronous Motors

Model-predictive control (MPC) is an optimization-based control technique. It has the benefits of being flexible and achieving a quick time response. However, this controller suffers from computational burden and sensitivity toward measurement noises, parametric variations, and model inaccuracies. Nowadays, the computation of MPC is no longer a problem, thanks to the new digital devices that exist on the market. However, robustness is still a major problem that complicates the usage of MPCs in applications, where the system model and parameters are not accurately known. A good example is the control of outer loops in cascaded control schemes. This paper presents multiple attempts to robustify the speed outer loop of a synchronous motor driven by a two-level power converter. An intuitive MPC speed outer-loop algorithm is first introduced. This first algorithm is weak against parametric variation, model inaccuracies, and measurement noises. Thus, a second more robust algorithm based on a torque balance expression is presented. This algorithm is robust toward parametric variations and model inaccuracies yet weak against measurement noises. Therefore, a subsequent improvement is added in a third algorithm in order to achieve a robust MPC controller. Furthermore, a least mean square identification algorithm is added to all control laws in order to identify the dynamical model parameters. These MPC controllers were experimentally tested and compared with a classic proportional–integral controller. Finally conclusions are drawn.

Robust sampled‐data model predictive control for networked systems with time‐varying delay

SummaryIn this paper, the problem of sampled‐data model predictive control (MPC) is investigated for linear networked control systems with both input delay and input saturation. The delay‐induced nonlinearity is overapproximatively modeled as a polytopic inclusion. The nonlinear behavior of input saturation is expressed as a convex polytope. The resulting closed‐loop systems are represented as linear systems with polytopic and additive norm‐bounded uncertainties. The aim is to determine a robust MPC controller that asymptotically stabilizes the uncertain system at the origin with a certain level of quadratic performance. The effectiveness of the proposed algorithm is demonstrated by a numerical example.

Delay-Range-Dependent Robust Constrained Model Predictive Control for Industrial Processes with Uncertainties and Unknown Disturbances

A delay-range-dependent robust constrained model predictive control is proposed for discrete-time system with uncertainties and unknown disturbances. The dynamic characteristic of the discrete-time system is established as a new extended state space model in which state variables and output tracking error are integrated and regulated independently. It is used as the design of control law of system, which cannot only guarantee the convergence and tracking performance but also offer more degrees of freedom for designed controller. Unlike the traditional robust model predictive control (RMPC), the novel, less conservative, and more simplified delay-range-dependent stable conditions are derived by linear matrix inequality (LMI) theory and some relaxed technologies, which make use of the information of the upper and lower bounds of the time-varying delay. Meanwhile, the H∞ performance index is introduced in the RMPC controller design, which can reject any unknown bounded disturbances. As a result, the design controller has better abilities of both tracking and disturbance rejection. The control results on the liquid level of tank system show that the proposed control method is effective and feasible.

On the coupling of model predictive control and robust Kalman filtering

Model predictive control (MPC) represents nowadays one of the main methods employed for process control in industry. Its strong suits comprise a simple algorithm based on a straightforward formulation and the flexibility to deal with constraints. On the other hand, it can be questioned its robustness regarding model uncertainties and external noises. Thus, a lot of efforts have been spent in the past years into the search of methods to address these shortcomings. In this study, the authors propose a robust MPC controller which stems from the idea of adding robustness in the prediction phase of the algorithm while leaving the core of MPC untouched. More precisely, they consider a robust Kalman filter that has been recently introduced and they further extend its usability to feedback control systems. Overall the proposed control algorithm allows to maintain all of the advantages of MPC with an additional improvement in performance and without any drawbacks in terms of computational complexity. To test the actual reliability of the algorithm, they apply it to control a servomechanism system characterised by non-linear dynamics.

Model Predictive Control meets robust Kalman filtering

Model Predictive Control (MPC) is the principal control technique used in industrial applications. Although it offers distinguishable qualities that make it ideal for industrial applications, it can be questioned its robustness regarding model uncertainties and external noises. In this paper we propose a robust MPC controller that merges the simplicity in the design of MPC with added robustness. In particular, our control system stems from the idea of adding robustness in the prediction phase of the algorithm through a specific robust Kalman filter recently introduced. Notably, the overall result is an algorithm very similar to classic MPC but that also provides the user with the possibility to tune the robustness of the control. To test the ability of the controller to deal with errors in modeling, we consider a servomechanism system characterized by nonlinear dynamics.

A novel tube model predictive control for surge instability in compressor system including piping acoustic

Tube model predictive control (MPC) is one of a few suitable techniques for robust stabilization of disturbed nonlinear systems subject to constraints. This paper introduces the integration of H∞ control scheme into a robust tube MPC control algorithm for surge prevention in centrifugal compressor system in the presence of bounded disturbances. Nonlinear dynamic of compression system is considered that contains acoustic of compressor system and brings up the effects of the station’s piping system on the compressor surge. Also, close-coupled valve is selected as actuator for the surge control system. The proposed method is composed of two controllers: a nominal MPC controller which solves a standard surge problem for the nominal system, and an ancillary MPC controller from H∞ control approach to stabilize the states despite disturbances. Numerical simulation results verify the capability of the proposed surge control method and guaranty the asymptotic stability of compression system in the presence of disturbances.

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

AbstractIn this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.