Explicit Nonlinear Model Predictive Control Research Articles

A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy

Advancements in electric vehicle technology have promoted the development trend of smart and low-carbon environmental protection. The design and optimization of electric vehicle braking systems faces multiple challenges, including the reasonable allocation and control of braking torque to improve energy economy and braking performance. In this paper, a multi-source braking force system and its control strategy are proposed with the aim of enhancing braking strength, safety, and energy economy during the braking process. Firstly, an ENMPC (explicit nonlinear model predictive control)-based braking force control strategy is proposed to replace the traditional ABS strategy in order to improve braking strength and safety while providing a foundation for the participation of the drive motor in ABS (anti-lock braking system) regulation. Secondly, a grey wolf algorithm is used to rationally allocate mechanical and electrical braking forces, with power consumption as the fitness function, to obtain the optimal allocation method and provide potential for EMB (electro–mechanical brake) optimization. Finally, simulation tests verify that the proposed method can improve braking strength, safety, and energy economy for different road conditions, and compared to other methods, it shows good performance.

Multiple-model adaptive explicit predictive control for nonlinear MIMO system

This work is to develop a blending-based multiple model adaptive explicit predictive control scheme for nonlinear MIMO systems that can handle parametric uncertainties. Here, for each identification model, an explicit nonlinear model predictive control (ENMPC) law is computed in advance for the corresponding model. The generated control inputs from the set of ENMPC controllers are being blended online using a weighting vector that is continuously updated by the proposed adaptive identification schemes. The proposed control scheme is used to govern the tracking of a highly nonlinear helicopter model known as the twin rotor MIMO system (TRMS). Here, an extended Kalman filter (EKF) is used to estimate the unavailable states of the TRMS. Finally, simulation and experimental results are presented to prove that the proposed controller gives better performance than some reported works in the literature. The effectiveness of the proposed controller is demonstrated by experimental studies of the TRMS model.

Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

AbstractTo promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.

Nonlinear Disturbance Observer Based Adaptive Explicit Nonlinear Model Predictive Control Design for a Class of Nonlinear MIMO System

In this paper, a nonlinear disturbance observer-based adaptive explicit nonlinear model predictive control scheme is proposed to compensate for external disturbance and parametric uncertainty for a class of nonlinear multi-input-multi-output (MIMO) systems. Here, the analytical solution of the proposed adaptive control scheme is developed by approximating the tracking errors and control efforts with the Taylor series expansion method. In this approach, a nonlinear disturbance observer is used to observe the unknown external disturbance of the system. To restrict the parameters from leaving the compact parameter space, an adaptive parameter estimator using projection-based parameter adaptation laws is used. The performance of the designed control technique is enhanced by incorporating the estimated disturbance and estimated system parameters in the updating control law. Using an aerodynamic laboratory set-up known as the twin-rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm has been verified. Simulation and real-time results show that the proposed control algorithm performs better than the existing control algorithm in the presence of unknown external disturbances and parameter uncertainties.

Multiparametric/explicit nonlinear model predictive control for quadratically constrained problems

Explicit model predictive control is an established methodology for the offline determination of the optimal control policy for linear discrete time-invariant systems with linear constraints. Nevertheless, nonlinearities in the form of quadratic constraints naturally appear in process models or are imposed for stability purposes in model predictive control formulations. In this manuscript, we present the theoretical developments and propose an algorithm for the exact solution of explicit nonlinear model predictive control problems with convex quadratic constraints. Our approach is based on a second-order Taylor approximation of Fiacco’s Basic Sensitivity Theorem, which allows for the existence and the analytic derivation of the optimal control actions. The complete exploration of the parameter space is founded on an active set strategy, which employs a pruning criterion to eliminate infeasible active sets. Based on that, the optimal map of solutions is constructed along with the corresponding control actions. The proposed strategy is applied to an explicit nonlinear model predictive control problem with an ellipsoidal terminal set, and comparisons with approximate solutions are drawn to demonstrate the benefits of the presented approach. Furthermore, as a practical application, the optimal operation of a chemostat in the presence of disturbances is exhibited.

Nonaffine Helicopter Control Design and Implementation Based on a Robust Explicit Nonlinear Model Predictive Control

Control design for a helicopter is a challenging problem because of its nonaffine inputs, its underactuated characteristics, and highly coupled dynamics. To solve a control problem of the helicopter under model uncertainties and disturbance present environments, an explicit nonlinear model predictive control (ENMPC), a dynamic inversion (DI), and an extended high-gain observer (EHGO) are combined in a multi-time-scale fashion. The multi-time-scale scaled structure and the ENMPC provide the framework of the control design, the DI deals with nonaffine control inputs, and the EHGO estimates the unmeasured system states and uncertainties. The proposed control design is discretized to be implemented on a small-scale helicopter. The successful outdoor experiments with the proposed control implemented on autopilot hardware demonstrate the validity of our approach in the presence of model uncertainties and wind disturbances.

A New Adaptive Explicit Nonlinear Model Predictive Control Design for a Nonlinear MIMO System: An Application to Twin Rotor MIMO System

This paper proposed an adaptive explicit nonlinear model predictive control (AENMPC) technique using multiple estimation models with a convex combination framework [18] for a class of nonlinear MIMO systems. Here, the explicit solution for the control signal is obtained from an optimal performance index which can be formulated without online optimization. In this work, a closed-form control law is developed by approximating the tracking error in the receding horizon by its Taylor series expansion. The control performance of any model-based control technologies explicitly depends on the quality of the unknown system parameters hence an adaptive parameter estimator is used to estimate the system parameter online [16,17]. To ensure the boundedness of the estimated parameter within a predefined compact region, a projection based adaptive law is used [43]. Using an aerodynamic laboratory set-up, known as the twin-rotor multi-input multi-output system (TRMS), the effectiveness of the proposed control algorithm has been verified. The complete state information of the system to the proposed adaptive controller is given from an extended Kalman filter based state observer. The performance of the proposed adaptive control algorithm has been verified successfully in simulations as well as real-time experimental setup of the TRMS model and compared with an existing control approach.

Explicit Nonlinear MPC for Fault Tolerance Using Interacting Multiple Models

This article presents a novel algorithm for adaptive explicit nonlinear model predictive control (eNMPC) with applications to fault tolerance. In order to account for plant-model mismatch, under which fault tolerance applies, the controller's explicit solution is designed with multiple dynamic models representing various operating modes as opposed to a single system model. Each model is weighted by a parameter variable to be evaluated online as mode probabilities produced by an interacting multiple model (IMM). Weighting each potential system model allows the controller to use a dynamic model that best matches the current operating mode, thus mitigating the degrading performance brought on by plant-model mismatch. The developed strategy is validated on attitude maneuvers for a nonlinear spacecraft system in the presence of disturbances and two actuator faults, which are indicative of the system mode. Average root mean squared values on the tracking error and control effort over Monte Carlo simulations are used to evaluate the effectiveness of the proposed techniques. Results indicate eNMPC benefits from access to weighted system models and manages similar levels of tracking error to standard spacecraft controllers at the same or minimal control effort.

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

Abstract We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from the observed system’s dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law’s parameters directly by backpropagating economic MPC loss through the learned system model. The control performance of the proposed DPC method is demonstrated in simulation using learned model of multi-zone building thermal dynamics.

A Real-Time Nonlinear CRPE Predictive PHEV Energy Management System Design and HIL Evaluation

The explicit nonlinear model predictive control (eNMPC) approach is a challenging yet encouraging prospective to design model-based and real-time controllers for complicated automotive applications. The precision of the nonlinear control-oriented model may contribute to the superior performance of the controller but adversely affect the real-time capability and even the convergence of optimization solution involved in such an approach. To address this challenge, control-relevant parameter estimation (CRPE) is used to ameliorate the capability of the nonlinear control-oriented model to exploit the cardinal dynamics of a complex plug-in hybrid powertrain. As such, an eNMPC energy management system is developed to be implemented in to an experimental hardware with fettered memory and computational capabilities. Hardware-in-the-Loop (HIL) simulation, which is conducted on a dSPACE MicroAutoBox unit along with sophisticated high-fidelity Autonomie model shows a superior performance of the proposed control scheme for various driving scenarios while maintaining real-time capability.

On Prediction Model Fidelity in Explicit Nonlinear Model Predictive Vehicle Stability Control

This study discusses vehicle stability control based on explicit nonlinear model predictive control (NMPC) and investigates the influence of prediction model fidelity on controller performance. The explicit solutions are generated through an algorithm using multiparametric quadratic programming (mp-QP) approximations of the multiparametric nonlinear programming (mp-NLP) problems. Controllers with different prediction models are assessed through objective indicators in sine-with-dwell tests. The analysis considers the following prediction model features: 1) nonlinear lateral tire forces as functions of slip angles, which are essential for the operation of the stability controller at the limit of handling. Moreover, a simple nonlinear tire force model with saturation is shown to be an effective alternative to a more complex model based on a simplified version of the Magic Formula; 2) longitudinal and lateral load transfers, playing a crucial role in the accurate prediction of the lateral tire forces and their yaw moment contributions; 3) coupling between longitudinal and lateral tire forces, which has a significant influence on the front-to-rear distribution of the braking forces generated by the controller; and 4) nonlinear peak and stiffness factors of the tire model, with visible yet negligible effects on the results.

Comparison of Anti-Jerk Controllers for Electric Vehicles With On-Board Motors

Anti-jerk controllers actively suppress the torsional oscillations of automotive drivetrains, caused by abrupt variations of the traction torque. The main benefits are: i) enhanced passengers’ comfort; and ii) increased component life. Extensive literature deals with the design of anti-jerk controllers for electric powertrains with on-board motors, i.e., in which the electric motor is part of the sprung mass of the vehicle, and transmits torque to the wheels through a transmission, half-shafts and constant velocity joints. Nevertheless, a complete and structured comparison of the performance of the different control options is still missing. This study addresses the gap through the assessment of six anti-jerk controllers – five exemplary formulations from the literature, and one novel formulation based on explicit nonlinear model predictive control (eNMPC). All proposed control structures have the potential to be implemented on production vehicles. A set of objective performance indicators is defined to assess the controllers, which are tuned through an optimization-based routine. Results show that the wheel speed input is critical to enhance controller performance, but may lead to reduced robustness.

Explicit nonlinear model predictive control tracking control based on a sliding mode observer for a quadrotor subject to disturbances

In this paper, we propose an explicit nonlinear model predictive control (ENMPC) method based on a robust observer to solve the trajectory tracking problem for outdoor quadrotors. We take into consideration the external aerodynamic disturbances present in the dynamics of the Newton-Euler quadrotor model. To overcome the effects of these disturbances, a high gain observer combined with a first order sliding mode observer are proposed to estimate both the states and the unknown disturbances using the only positions and angular measurements of the quadrotor. The estimated signals are then used by the predictive controller in order to ensure the trajectory tracking objective. Despite the presence of bounded disturbances, the convergence of the composite controller (ENMPC technique with the latter observers) is guaranteed through a stability analysis. Theoretical results are validated with some numerical simulations showing the good performances of the proposed tracking control approach.

Explicit Nonlinear Model Predictive Control for Electric Vehicle Traction Control

This paper presents a traction control (TC) system for electric vehicles with in-wheel motors, based on explicit nonlinear model predictive control. The feedback law, available beforehand, is described in detail, together with its variation for different plant conditions. The explicit controller is implemented on a rapid control prototyping unit, which proves the real-time capability of the strategy, with computing times on the order of microseconds. These are significantly lower than the required time step for a TC application. Hence, the explicit model predictive controller can run at the same frequency as a simple TC system based on proportional integral (PI) technology. High-fidelity model simulations provide: 1) a performance comparison of the proposed explicit nonlinear model predictive controller (NMPC) with a benchmark PI-based traction controller with gain scheduling and anti-windup features, and 2) a performance comparison among two explicit and one implicit NMPCs based on different internal models, with and without consideration of transient tire behavior and load transfers. Experimental test results on an electric vehicle demonstrator are shown for one of the explicit NMPC formulations.

Nonlinear MPC for a Sensorless Multi‐Vectored Propeller Airship Based on Sliding Mode Observer with Saturation

AbstractA nonlinear fault tolerant station keeping controller for a multi‐vectored propeller airship without velocity and angular velocity sensors is developed, which is composed of three modules: nonlinear model predictive controller (NMPC), sliding mode observer (SMO), and linear programming (LP) based control allocation. The kinematics and dynamics model of the airship are introduced. Based on the nonlinear model, with the assumption that the velocity and angular velocity sensors are damaged, a sliding mode observer is designed to estimate the velocity and angular velocity of the airship. To achieve good performance in the station keeping mission, an explicit nonlinear model predictive control is derived. A linear programming base control allocation method is proposed to solve both amplitude and rate constraint of the propulsion forces and deflection angles. Stability analysis is carried out to prove that the system can be stabilized in finite time. Simulation results for the station keeping control are illustrated to prove the effectiveness of the proposed method.

Model predictive control (MPC) strategies for PEM fuel cell systems – A comparative experimental demonstration

The aim of this work is to demonstrate the response of advanced model-based predictive control (MPC) strategies for Polymer Electrolyte Membrane Fuel cell (PEMFC) systems. PEMFC are considered as an interesting alternative to conventional power generation and can be used in a wide range of stationary and mobile applications. An integrated and modular computer-aided Energy Management Framework (EMF) is developed and deployed online to an industrial automation system for monitoring and operation of a PEMFC testing unit at CERTH/CPERI. The operation objectives are to deliver the demanded power while operating at a safe region, avoiding starvation, and concurrently minimize the fuel consumption at stable temperature conditions. A dynamic model is utilized and different MPC strategies are online deployed (Nonlinear MPC, multiparametric MPC and explicit Nonlinear MPC). The response of the MPC strategies is assessed through a set of comparative experimental studies, illustrating that the control objectives are achieved and the fuel cell system operates economically and at a stable environment regardless of the varying operating conditions.

Surge explicit nonlinear model predictive control using extended Greitzer model for a CCV supported compressor

ABSTRACTThis paper indicates the use of explicit nonlinear model predictive control method to prevent and control of compressor surge using extended Greitzer model. To encompass the effects of fast transients, nonlinear extended Greitzer model is considered for modelling and control of the compressor system. This model covers the effects of different parts, especially the compressor system pipeline, as the most important factor in the occurrence and acceleration of the surge. Also, the mathematical description of the flow dynamic of compression system is derived in the presence of close-coupled valve (CCV) as the most commonly used actuator. For controlling the compressor system surge instability, explicit nonlinear model predictive control (NMPC) is applied, whose allows efficient online implementation, significantly enlarges the operating region of the compressor and enhances the authority of the control system. Numerical simulations show that the proposed control system is able to meet the desired specifications in avoiding and active control of surge, in the presence of different types of disturbances occurring along the pipeline.Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka.

Design of Explicit Model Predictive Controllers Based on Orthogonal Partition of the Parameter Space: Methods and A Software Tool

This paper reviews the approaches to explicit approximate Nonlinear Model Predictive Control (NMPC), based on orthogonal partition of the parameter space. They are classified with respect to the type of control problem, the type of model describing the nonlinear system, the presence of uncertainty, the type of control input, and the type of the approximating control function. A software tool for design of explicit NMPC by applying the described approaches is presented. It is used to design an explicit NMPC controller for a continuous stirred tank reactor.

Correcting hypothalamic-pituitary-adrenal axis dysfunction using observer-based explicit nonlinear model predictive control.

The hypothalamic-pituitary-adrenal (HPA) axis is critical in maintaining homeostasis under physical and psychological stress by modulating cortisol levels in the body. Dysregulation of cortisol levels is linked to numerous stress-related disorders. In this paper, an automated treatment methodology is proposed, employing a variant of nonlinear model predictive control (NMPC), called explicit MPC (EMPC). The controller is informed by an unknown input observer (UIO), which estimates various hormonal levels in the HPA axis system in conjunction with the magnitude of the stress applied on the body, based on measured concentrations of adreno-corticotropic hormones (ACTH). The proposed closed-loop control strategy is tested on multiple in silico patients and the effectiveness of the controller performance is demonstrated.

Explicit Nonlinear Model Predictive Control for a Saucer-Shaped Unmanned Aerial Vehicle

A lifting body unmanned aerial vehicle (UAV) generates lift by its body and shows many significant advantages due to the particular shape, such as huge loading space, small wetted area, high-strength fuselage structure, and large lifting area. However, designing the control law for a lifting body UAV is quite challenging because it has strong nonlinearity and coupling, and usually lacks it rudders. In this paper, an explicit nonlinear model predictive control (ENMPC) strategy is employed to design a control law for a saucer-shaped UAV which can be adequately modeled with a rigid 6-degrees-of-freedom (DOF) representation. In the ENMPC, control signal is calculated by approximation of the tracking error in the receding horizon by its Taylor-series expansion to any specified order. It enhances the advantages of the nonlinear model predictive control and eliminates the time-consuming online optimization. The simulation results show that ENMPC is a propriety strategy for controlling lifting body UAVs and can compensate the insufficient control surface area.