Linear and Non-linear Multi-Input Multi-Output Model Predictive Control of Continuous Stirred Tank Reactor

In this paper a hierarchical model predictive control framework for the energy management of a hybrid electric vehicle is extended by replacing the supervisory linear model predictive controller with a nonlinear model predictive controller. The nonlinear system dynamics of a parallel hybrid electric vehicle are incorporated into a nonlinear optimal control problem which is solved at each time instance. The discretization of the continuous time system dynamics is realized via direct multiple shooting. The low-level linear model predictive controller considers the actuator dynamics for optimal tracking of the driver's torque demand while the high-level controller considers the slow dynamics of the vehicle and the battery. The proposed strategy is validated in simulation with the worldwide harmonized light vehicles test cycle and compared to a hierarchical model predictive control framework with linearized system dynamics.

An important feature of linear model predictive control (MPC) is the ability to provide offset-free control through integral action. Linear MPC can utilize a steady-state target optimizer (SSTO) in conjunction with a dynamic optimization in order to manage systems that are non-square, have integrating modes, or encounter infeasible setpoints. Integral action does not ensure that the feasible steady-state target is closest to the true optimum when the desired setpoint is infeasible. This paper describes the modifications necessary to linear state-space MPC algorithms in order to address this problem (assuming systems with no integrating modes). The solution employs features of the integrated system optimization and parameter estimation (ISOPE) algorithm: the SSTO cost is modified by a term that results in matching of the true plant and model conditions necessary for optimality. This work combines well with prior work which has determined the situations where the modification is actually necessary.

This paper presents a novel function of energy-optimal adaptive cruise control (EACC) for electric vehicles based on model predictive control (MPC), which optimally plans the host car's speed trajectory for higher energy efficiency through taking the surrounding traffic information and the road conditions ahead into account. To cope with the nonlinearity of the system dynamics, nonlinear MPC (NMPC) is designed in this paper. Afterwards, the nonlinear equality constraints are relaxed so that the optimization problem has a convex feasible set. Moreover, it is proven that the nonlinear problem can be recast as a second-order cone programming (SOCP) problem. The performance of NMPC is evaluated in the real driving condition and compared to both linear MPC and receding horizon dynamic programming (RH-DP). In order to enable real-time control, the interior point method is used to solve both linear and nonlinear MPC problems and the computation time is investigated in this paper.

An off-line Model Reduction-based Technique for On-line Linear MPC Applications for Nonlinear Large-Scale Distributed Systems

Given the highly nonlinear and strongly constrained nature of the electro-hydraulic system, we proposed an observer-based approximate nonlinear model predictive controller (ANMPC) for the trajectory tracking control of robotic excavators. A nonlinear non-affine state space equation with identified parameters is employed to describe the dynamics of the electro-hydraulic system. Then, to mitigate the plant-model mismatch caused by the first-order linearization, an approximate affine nonlinear state space model is utilized to represent the explicit relationship between the output and input and an ANMPC is designed based on the approximate nonlinear model. Meanwhile, the Extended Kalman Filter was introduced for state observation to deal with the unmeasurable velocity information and heavy measurement noises. Comparative experiments are conducted on a 1.7-ton hydraulic robotic excavator, where ANMPC and linear model predictive control are used to track a typical excavation trajectory. The experimental results provide evidence of convincing trajectory tracking performance.

This article proposes an energy management system (EMS) for a fuel cell (FC) hybrid electric vehicle. The EMS is based on nonlinear model predictive control (NMPC) and employs a recurrent neural network (RNN) for modeling a proton exchange membrane FC. The NMPC makes possible the formulation of control objectives not allowed by a linear model predictive control (MPC), such as maximum efficiency point tracking of the FC, while the RNN can accurately predict the FC nonlinear dynamics. The EMS was implemented on a low-cost development board, and the experiments were performed in real time on a hardware-in-the-loop test bench equipped with a real 3-kW FC stack. The experimental results demonstrate that the NMPC EMS is able to meet the vehicle's energy demand, as well as to operate the FC in its most efficient region. Moreover, a comparative study is performed between the proposed NMPC, a linear MPC, and hysteresis band control. The results of this comparative study demonstrate that the NMPC provides a better fuel economy and can reduce FC degradation.

Conditions for offset elimination in state space receding horizon controllers: A tutorial analysis

Wiener model identification and predictive control of a pH neutralisation process is presented. Input-output data from a nonlinear, first principles simulation model of the pH neutralisation process are used for subspace-based identification of a black-box Wiener-type model. The proposed nonlinear subspace identification method has the advantage of delivering a Wiener model in a format which is suitable for its use in a standard linear-model-based predictive control scheme. The identified Wiener model is used as the internal model in a model predictive controller (MPC) which is used to control the nonlinear white-box simulation model. To account for the unmeasurable disturbance, a nonlinear observer is proposed. The performance of the Wiener model predictive control (WMPC) is compared with that of a linear MPC, and with a more traditional feedback control, namely a PID control. Simulation results show that the WMPC outperforms the linear MPC and the PID controllers.

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

A roadmap for in silico development and evaluation of industrial NMPC applications: A practical case study

Model predictive control (MPC) has become a practical approach for implementing active safety control strategies in autonomous vehicles (AVs). This paper introduces a Fast Iterative MPC (FI-MPC) framework with rule-based iteration convergence criteria to tackle the significant challenges of control precision and solving time discrepancies between linear and nonlinear MPC algorithms within tracking control strategies for AVs. Differing from linear and nonlinear MPC structures, the core concept of FI-MPC involves incorporating the unmodeled nonlinear dynamics of the vehicle or tires into a linear framework to achieve optimal iterative control solutions. The goal is to mitigate the mismatch between linear and high-fidelity nonlinear dynamics models, thus achieving real-time high-precision tracking control of nonlinear vehicle dynamics under challenging conditions. In addition, rule-based convergence criteria are designed to enhance the iteration mechanism of FI-MPC, further conserving the computational resources of the onboard controller by reducing unnecessary iteration steps. To validate the effectiveness of the FI-MPC algorithm, this study investigates the trajectory tracking problem for a four-wheel-drive AV for a weave test scenario. Co-simulation and hardware-in-the-loop testing results at various speeds confirm that FI-MPC enables high-precision control of nonlinear dynamics while ensuring excellent real-time performance.

This paper deals with the application of interval arithmetic to non linear model predictive control (NMPC) problem. The NMPC problem is expressed as a constraints satisfaction problem (CSP) which can be solved by interval analysis techniques. We present the classical interval techniques to build a nonlinear model predictive control law and propose some improvements in order to adapt interval tools to the context of control. Moreover, in order to reduce the pessimism introduced by interval state estimation, we propose a spatial discretisation of the input. These methods are illustrated on a inverted pendulum model.

Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control

Roller compaction is the major process of dry granulation which is attractive to heat or moisture-sensitive pharmaceutical products. Currently, the product quality of roller compaction is analyzed off-line in the quality control lab. In this work, we demonstrate how online process control can be applied on roller compaction using the simulator built in Part I of this paper. Different control strategies are discussed: multi-loop proportional–integral–derivative, linear model predictive control (MPC), and nonlinear MPC. The MPC strategy provides a systematic approach to design the multivariable control system. The simulation results show that the linear MPC can serve as a high-performance control strategy for roller compaction with the trade-off between the control performance and computational complexity. Such enhanced process control facilitates the FDA’s process analysis technology initiative.

Combining CSP and MPC for the operational control of water networks