Nonlinear model predictive control strategy for vehicle path tracking with steering actuator’s dynamic characteristics

<div class="section abstract"><div class="htmlview paragraph">This paper investigates the problem of nonlinear model predictive control (NMPC) strategy for a class of nonlinear systems with multiple actuators’ response time-delays. Conventional approaches that incorporate these time-delays into the NMPC formulation typically result in a significant increase in the optimization problem's scale. To address these problems, we propose a novel NMPC strategy. In the first stage, the NMPC strategy is designed for the nonlinear system without considering actuator’s response time-delay, thereby maintaining the original scale of the optimization problem. The optimal control sequence derived from this NMPC is then fitted to a time-continuous polynomial function, serving as a reference signal for the actuators' response time-delay models. In the second stage, combining inverse model and inverse Laplace transform techniques, a novel inverse model compensation control (IMCC) strategy is designed for actuators’ response time-delays. This IMCC strategy enables tracking of the reference signal without phase time-delay or amplitude deviation. For comparative analysis, we also implement a model augmentation NMPC strategy that directly incorporates actuators’ time-delays, inevitably increasing the scale of the optimization problem. By quantitative analysis, the model augmentation NMPC strategy will increase the number of optimal variables and equality constraints of the optimization problem. Finally, vehicle control of transport vehicle in open-pit mine is taken as simulation example, the simulation results show that both the proposed novel NMPC and IMCC algorithms and model augmentation NMPC algorithm can achieve high precision control performance, the maximum and average calculation time of the proposed novel NMPC and IMCC algorithms are 31.9% and 46.2% lower than that of model augmentation NMPC algorithm, respectively.</div></div>

A novel nonlinear model predictive control (NMPC) strategy for path tracking of autonomous vehicles with stable limit handling is proposed in this article. To improve the path tracking performance under complex driving maneuvers, a tire lateral force model, which treats road adhesion coefficient and vertical load as variable parameters, is discussed first. It has the advantage that the dynamics model can be applied under different driving conditions. In addition, the stability properties of the dynamics system with the front tire lateral force as the virtual control input are analyzed. The global asymptotical stability with zero input and local input-to-state stability with nonzero input of the dynamics system are proved respectively. To perform path tracking within the handling limits, both constraints of front tire lateral force and rear tire slip angle are included in the NMPC controller. The constraint of front tire lateral force is considered as peak limits related to load transfer and adhesion coefficient. And for the rear tire slip angle, a combining constraint scheme is proposed, where the indirect constraint is implemented by a penalty term that predicts the saturation of rear tire lateral force, while the direct constraint is implemented by a dead-zone exponential penalty function. The Continuation/Generalized Minimum Residual (C/GMRES) algorithm is applied to improve the computation efficiency of the NMPC. The performance of the controller is evaluated in simulations and hardware-in-the-loop (HIL) tests, and the results show that the controller is able to track the reference path with high precision in real-time.

ABSTRACTThis paper briefly reviews development of nonlinear model predictive control (NMPC) schemes for finite horizon prediction and basic computational algorithms that can solve the stable real‐time implementation of NMPC in space state form with state and input constraints. In order to ensure stability within a finite prediction horizon, most NMPC schemes use a terminal region constraint at the end of the prediction horizon — a particular NMPC scheme using a terminal region constraint, namely quasi‐infinite horizon, that guarantees asymptotic closed‐loop stability with input constraints is presented. However, when nonlinear processes have both input and state constraints, difficulty arises from failure to satisfy the state constraints due to constraints on input. Therefore, a new NMPC scheme without a terminal region constraint is developed using soften state constraints. A brief comparative simulation study of two NMPC schemes: quasi‐infinite horizon and soften state constraints is done via simple nonlinear examples to demonstrate the ability of the soften state constraints scheme. Finally, some features of future research from this study are discussed.

This work establishes the feasibility of using a multilayer perceptron for the development of a multimodel that combines structurally simple local models developed in different operating regions. The local models either are obtained by linearizing a first principles model or are identified from input−output data using a linear combination of Laguerre filters. In particular, it is shown that the proposed multimodels can capture dynamic and steady-state characteristics of a continuous fermenter, which exhibit input multiplicities and change in the sign of steady-state gains, fairly accurately over a wide operating range. The proposed multimodel is further used to develop a nonlinear model predictive control (NMPC) scheme. The effectiveness of the NMPC scheme is demonstrated by simulating a servo problem that requires the fermenter to be controlled at its optimum operating point, which happens to be singular points where the invertibility is lost. The proposed NMPC scheme is found to achieve a smooth transition for large-magnitude setpoint changes and control the systems at the singular operating point even in the presence of measurement noise. The NMPC scheme is also found to be robust to moderate variations in system parameters.

Hybrid electric vehicles have received considerable attention because of their ability to improve fuel consumption compared to conventional vehicles. In this paper, a series-parallel hybrid electric vehicle is used because they combine the advantages of the other two configurations. In this paper, the control unit for a series-parallel hybrid electric vehicle is implemented using a Nonlinear Model Predictive Control (NMPC) strategy. The NMPC strategy needs to create a vehicle energy management optimization problem, which consists of the cost function and its constraints. The cost function describes the required control objectives, which are to improve fuel consumption and obtain a good dynamic response to the required speed while maintaining a stable value of the state of charge (SOC) for batteries. While the cost function is subject to the physical constraints and the mathematical prediction model that evaluate the vehicle’s behavior based on the current vehicle measurements. The optimization problem is solved at each sampling step using the (SQP) algorithm to obtain the optimum operating points of the vehicle’s energy converters, which are represented by the torque of the vehicle components.

This chapter proposes a nonlinear model predictive control (NMPC) strategy for WDNs including both flow and pressure constraints. A WDN might be regarded as a nonlinear system described by differential-algebraic equations (DAEs), when flow and hydraulic head equations are considered in the model. The main operational goal of WDNs is the minimization of the economic costs associated with pumping. In addition to the minimization of costs, the optimal operation of WDNs should guarantee water supply with required flows and pressures at all the control/demand nodes in the network. Other operational goals related to safety and reliability are usually sought. From a control point of view, NMPC is a suitable control strategy for WDNs, since the optimal operation of the network cannot be established a priori by fixing reference volumes in the tanks. Alternatively, the NMPC strategy should determine the optimal filling/emptying sequence of the tanks taking into account that electricity price varies between day and night and that the demand also follows a 24-h repetitive pattern. On the other hand, as a result of the ON/OFF operation of pumps in pumping stations, a two-layer control scheme has been utilized: the NMPC strategy at the hourly sampling timescale is chosen in the upper layer while the pump scheduling approach at the minutely sampling timescale dealing with pumps in the ON/OFF manner is proposed in the lower layer. Finally, results of applying the proposed control strategy to a portion of the Barcelona WTN are provided in simulation.

This thesis aims at the investigation and development of the control of waste heat recovery systems (WHR) for heavy duty trucks based on the organic Rankine cycle. It is desired to control these systems in real time so that they recover as much energy as possible, but this is no trivial task since their highly nonlinear dynamics are strongly affected by external inputs (disturbances). Additionally, nonlinear operational constraints must be satisfied. To deal with this problem, in this thesis a dynamic model of a WHR that is based on first principles and empirical relationships from thermodynamics and heat transfer is formulated. This model corresponds to a DAE of index 1. In view of the requirements of the employed numerical methods, it includes a spline-based evaluation method for the thermophysical properties needed to evaluate the model. Therewith, the continuous differentiability of the state trajectories with respect to controls and states on its domain of evaluation is achieved. Next, an optimal control problem (OCP) for a fixed time horizon is formulated. From the OCP, a nonlinear model-predictive control (NMPC) scheme is formulated as well. Since NMPC corresponds to a state feedback strategy, a state estimator is also formulated in the form of a moving horizon estimation (MHE) scheme. In this thesis, we make use of efficient numerical methods based on the direct multiple shooting (DMS) method for optimal control, backward differentiation formulae for the solution of initial value problems for DAE, and the corresponding versions of the real-time iteration (RTI) scheme in order to approximately solve the OCP and implement the MHE and NMPC schemes. The simultaneous implementation of NMPC and MHE schemes based on RTI has been already proven to be stable in the control literature. Several numerical instances of the DMS method for the proposed OCP, NMPC and MHE schemes are tested assuming a given real-world operation scenario consisting of truck exhaust gas data recorded during a real trip. These data have been kindly provided by our industry cooperation partner Daimler AG. Additionally, the PI and LQGI control strategies, of wide-spread use in the literature of control of WHR, are also considered for comparison with the proposed scheme. An important result of this thesis is that, considering the highest energy recovery obtained from both strategies as a reference for the given operation scenario, the proposed NMPC scheme is able to reach an additional energy generation of around 3% when the full state vector is assumed to be known, and its computational speed allows it to update the control function in times shorter than the considered sampling time of 100 [ms], which makes it a suitable candidate for real-time implementation. In a more realistic scenario in which the state has to be estimated from noisy measurements, a combination of both aforementioned NMPC and MHE schemes yields an additional energy generation of around 2%. Concretely, this thesis presents novel results and advances in the following areas: • A first principles DAE model of the WHR is presented. The model is derived from the energy and mass conservation considerations and empirical heat transfer relationships; and features a tailored evaluation method of thermophysical properties with which it possesses the property of being at least continuously differentiable with respect to its controls and states on its whole domain of evaluation. • A new real-time optimization control strategy for the WHR is developed. It consists of an NMPC strategy based on efficient simulation, optimization and control tools developed in previous works. The scheme is able to explicitly handle nonlinear constraints on controls and states. In contrast to other NMPC instances for the WHR found in the literature, our scheme's efficient numerical treatment make it real-time feasible even if the full nonlinear WHR dynamics are considered. • To the author's knowledge, this is the first implementation that considers both the NMPC and the MHE approaches used simultaneously in the control of the WHR. The combination of NMPC and MHE produces a closed-loop, model-based implementation that can treat realistic measurements as inputs and calculates the corresponding control functions as outputs.

Nonlinear Model Predictive Control of a Vapor Compression Cycle based on First Principle Models

Batch reactors are widely used in the production of fine chemicals, polymers, pharmaceuticals and other specialty products. For certain exothermic reactions, the transient operation of the reactor with respect to small changes in critical parameters like coolant temperature and initial composition of the reactants can lead runaway condition of the reactor. In order to avoid the hazards associated with runaway situations, it is imperative to operate the reactor by means of an efficient controller. This work presents a nonlinear model predictive control (NMPC) strategy based on simulated annealing (SA) for the temperature control of a batch reactor involving a highly exothermic runaway reaction. The efficacy of the proposed strategy is studied through simulation for the temperature control of the reactor in which a highly parametric sensitive exothermic reaction of hydrolysis of acetic anhydride with sulfuric acid as catalyst and acetic acid as a solvent is carried out. The controller is found effective in averting the runaway behavior with the smooth and quick attainment of the desired operating condition. The results demonstrate the better performance of the SA based NMPC over the linear model predictive controller (LMPC).

Improving performance and increasing process profitability represent a priority for the long‐term operation of the crude oil distillation process. To increase process profitability and maintain control performance, in this paper, an improved economic‐based nonlinear model predictive control (NMPC) strategy is used to optimize the crude oil distillation (CDU) process. Considering the strong coupling and nonlinear dynamics of the CDU process, we make some modifications for the existing NMPC strategy. To reduce the complexity of the nonlinear prediction model, a support vector regression (SVR) based model is employed to describe the dynamical behaviour of the CDU process. Considering the coupling of the CDU process, we propose the concept of the coupling weighting factor to modify the objective function of the NMPC optimization problem. The simulation results demonstrate the effectiveness of the proposed improved NMPC algorithm for the CDU process.

In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example. This paper is an extended version of the accepted paper [1], and contains additional details regarding \textit{robust} trajectory tracking (App.~B), continuous-time dynamics (App.~C), output tracking stage costs (App.~D) and the connection to incremental system properties (App.~A).

Stabilization of gas-lift oil wells by a nonlinear model predictive control scheme based on adaptive neural network models

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

This paper addresses the problem of cooperative transportation of an object rigidly grasped by N robotic agents. In particular, we propose a Nonlinear Model Predictive Control (NMPC) scheme that guarantees the navigation of the object to a desired pose in a bounded workspace with obstacles, while complying with certain input saturations of the agents. Moreover, the proposed methodology ensures that the agents do not collide with each other or with the workspace obstacles as well as that they do not pass through singular configurations. The feasibility and convergence analysis of the NMPC are explicitly provided. Finally, simulation results illustrate the validity and efficiency of the proposed method.

SummaryThis article addresses the problem of designing a sensor fault‐tolerant controller for an observation process where a primary, controlled system observes, through a set of measurements, an exogenous system to estimate the state of this system. We consider sensor faults captured by a change in a set of sensor parameters affecting the measurements. Using this parametrization, we present a nonlinear model predictive control (NMPC) scheme to control the observation process and actively detect and estimate possible sensor faults, with adaptive controller reconfiguration to optimize the use of the remaining sensing capabilities. A key feature of the proposed scheme is the design of observability indices for the NMPC stage cost to improve the observability of both the state of the exogenous system and the sensor fault parameters. The effectiveness of the proposed scheme is illustrated through numerical simulations.