Nonlinear Model Predictive Control Approach Research Articles

Nonlinear model predictive control of a climatization system using rigorous nonlinear model

Buildings are known for being great consumers of energy and for operating under On/Off and linear control strategies in common commercial packages. In order to reduce their energy footprints and to improve thermal comfort, new methodologies are needed to obtain better input profiles. This paper presents a detailed study of the implementation of a nonlinear model predictive control (NMPC) approach for a heating, ventilation, and air conditioning (HVAC) system. The HVAC system is modeled by an index-1 differential-algebraic system of equations, obtained from rigorous material and energy balances. The proposed NMPC algorithm was implemented in GAMS and compared with another approach from the literature. Similarly, the objective function is defined using one or more of the following criteria: (1) tracking of temperature and relative humidity set points; (2) maximization of thermal comfort; (3) minimization of energy consumption. To better represent the situation in a real application, the simulations include model-plant mismatch in parameters such as air infiltration into the building, the coefficient of the thermal exchange between the building and the exterior, and occupancy level. Additionally, simulations with random measurement noise have been performed. The results have shown that the proposed approach, in which the model is not linearized at any step, is able to reduce the energy consumption and maintain the Predicted Mean Vote (PMV) close to the desired set point, while the computation burden is only increased by one second per iteration, which is negligible in comparison with a sampling time of 10 min.

Autonomous Driving Based on Nonlinear Model Predictive Control and Multi-Sensor Fusion

Abstract Algorithms for controlling fully autonomous systems must meet especially high requirements with respect to safety and robustness. A particularly challenging example are autonomous deep space missions, which we investigated in several projects. In this context, we showed that a safe and robust autonomous system can be realized through nonlinear model predictive control approaches using optimization techniques in combination with multi-sensor fusion based on an extended representation of uncertainty. The focus of this paper is on demonstrating the versatility of that concept by transferring the corresponding algorithms to the also very challenging application of autonomous driving. In particular, we propose a system concept for a self-driving car based on our methodology. Furthermore, we present results of a real world research vehicle that autonomously explores a parking lot, dynamically takes obstacles into account, and finally performs a parking maneuver.

Preliminary study for motion sickness reduction in autonomous vehicles: an MPC approach

This study shows a new method for evaluating the optimal speed profile for a given route. The article deals with the feasibility of autonomous driving (AD) strategies that take into account passenger comfort, focusing on the motion sickness (MS) phenomenon. In this paper a Non-linear Model Predictive Control (NMPC) approach is used to model a vehicle moving along a predefined route; the vehicle is modelled using a point mass model and is assumed to move along a spline. Literature models are used to model MS. The Model Predictive Control (MPC) used is non-linear because the model of this article is integrated in the space domain instead of a traditional integration in the time domain; this approach is shown in several papers concerning autonomous driving control. The main contribution of this study is to implement quantitatively the consideration of comfort in autonomous driving. In the literature, the articles related to comfort in AD address the problem in a qualitative way and those related to AD control techniques analyse the problem considering only the vehicle dynamics. Another contribution is to present the spatial transformation of MS models in the literature, allowing an easier implementation of these models in AD control. The results of this introductory analysis show how MS can be reduced by minimizing the increase in travel times. This technique can be used in AD or advanced driving assistance systems (ADAS) to create less nauseogenic systems or can also be used in traditional driving by advising the human driver with the best speed profile to reduce MS.

Robust NMPC using a model-error model with additive bounds to handle structural plant-model mismatch

Abstract We address the problem of robust nonlinear model predictive control (NMPC) under structural plant model mismatch in a multi-stage framework using a model-error model (MEM). Multi-stage NMPC models the presence of future feedback information in the predictions, hence it is less conservative than the other existing robust NMPC approaches. MEM consists of a stable linear model, an unknown nonlinear operator with bounded gain and a bounded additive mismatch. The computational burden of the proposed scheme is reduced by using two different approximations; 1. Constraint tightened multi-stage NMPC 2. Tube-enhanced multistage NMPC. Both the schemes are real-time implementable with a small loss in performance when compared to the standard multi-stage NMPC. The advantages of the proposed schemes are demonstrated for a benchmark continuous stirred tank reactor (CSTR) example.

Dynamic Optimization and Non-linear Model Predictive Control to Achieve Targeted Particle Morphologies.

An event‐driven approach based on dynamic optimization and nonlinear model predictive control (NMPC) is investigated together with inline Raman spectroscopy for process monitoring and control. The benefits and challenges in polymerization and morphology monitoring are presented, and an overview of the used mechanistic models and the details of the dynamic optimization and NMPC approach to achieve the relevant process objectives are provided. Finally, the implementation of the approach is discussed, and results from experiments in lab and pilot‐plant reactors are presented.

Adaptive Tube-Based Nonlinear MPC for Economic Autonomous Cruise Control of Plug-In Hybrid Electric Vehicles

This paper proposes an adaptive tube-based nonlinear model predictive control (AT-NMPC) approach to the design of autonomous cruise control (ACC) systems. The proposed method utilizes two separate models to define the constrained receding horizon optimal control problem. A fixed nominal model is used to handle the problem constraints based on a robust tube-based approach. A separate adaptive model is used to define the objective function, which utilizes least square online parameter estimators for adaption. By having two separate models, this method takes into account uncertainties, modeling errors and delayed data in the design of the controller and guaranties robust constraint handling, while adapting to them to improve control performance. Furthermore, to be able implement the designed AT-NMPC in real-time, a Newton/GMRES fast solver is employed to solve the optimization problem. Simulations performed on a high-fidelity model of the baseline vehicle, the Toyota plug-in Prius, which is a plug-in hybrid electric vehicle (PHEV), show that the proposed controller is able to handle the defined constraints in the presence of uncertainty, while improving the energy cost of the trip. Moreover, the result of the hardware-in-loop experiment demonstrates the performance of the proposed controller in real time application.

Minimum control effort–based path planning and nonlinear guidance for autonomous mobile robots

This article puts forth a framework using model-based techniques for path planning and guidance for an autonomous mobile robot in a constrained environment. The path plan is synthesized using a numerical navigation function algorithm that will form its potential contour levels based on the “minimum control effort.” Then, an improved nonlinear model predictive control approach is employed to generate high-level guidance commands for the mobile robot to track a trajectory fitted along the planned path leading to the goal. A backstepping-like nonlinear guidance law is also implemented for comparison with the NMPC formulation. Finally, the performance of the resulting framework using both nonlinear guidance techniques is verified in simulation where the environment is constrained by the presence of static obstacles.

Decentralized nonlinear model predictive control of a multimachine power system

This paper proposes a novel decentralized nonlinear model predictive control approach for excitation control in multimachine power systems. A key feature of the proposed approach is the reduction of the multimachine control problem to multiple single-machine control problems. These reduced size control problems only require direct measurements from individual generators, thereby making implementation simple in practice. The effectiveness of the proposed approach is demonstrated through computer simulations on a one small-size Western System Coordinating Council (WSCC) and one large-size New England power system under a wide range of operating conditions. The performance of the proposed approach is evaluated in terms of damping power system oscillations, critical time enhancement, and control signal energy consumption. The results are compared with those obtained using power system stabilizer and feedback linearization based control schemes and found to be impressive.

Actuator failure‐tolerant control of an all‐thruster satellite in coupled translational and rotational motion using neural networks

SummaryThe nonlinear model predictive control (MPC) approach is used to control the coupled translational‐rotational motion of an all‐thruster spacecraft when one of the actuators fails. In order to model the dynamical response of the spacecraft in MPC, instead of direct integration, a neural network (NN) model is utilized. This model is built of a static NN, followed by a dynamic NN. The static NN is used to find the changes of the mapping of “the demanded forces to the thrusters” and “the real torques/forces produced by the remaining thrusters” after the failure occurrence through online training. In this manner, the effect of failed thruster on the dynamics can be found and the need for conventional and separate “fault detection and isolation” in previous works is eliminated. The dynamic NN is used to replicate the dynamical equations of the spacecraft excluding the effects of the mapping of thrusters demand to the real generated force and torque. Using updated model of the spacecraft through the learning capability of the NNs, the nonlinear MPC is able to compensate the failure of the thruster with the help of the remaining active thrusters. Through numerical simulations, it is shown that in the presence of thruster failure(s) this approach can effectively control the spacecraft with the remaining actuators.

Nonlinear model predictive energy management of hydrostatic drive transmissions

In this article, we devise a nonlinear model predictive control framework for the energy management of nonhybrid hydrostatic drive transmissions. The controller determines the optimal control commands of the actuators by minimising a cost function over a receding horizon. With our approach, the velocity-tracking error is minimised while keeping the fuel economy of the system high. The hydrostatic drive transmission system studied in this article is a typical commercial work machine, that is, there is no energy storage or alternative power source in the system (a nonhybrid hydrostatic drive transmission). We evaluate success with a validated simulation model of the hydrostatic drive transmission of a municipal tractor. In our experiments, a detailed system model is used both in the system simulation and in the prediction phase of the nonlinear model predictive control. The use of a detailed model in the nonlinear model predictive control framework places our design as a benchmark for controlling nonhybrid hydrostatic drive transmissions, when compared to solutions using simplified models or computationally less intensive control methods as in earlier work by the authors. Our nonlinear model predictive control approach enables numerically robust optimisation convergence with the utilised complex nonlinear model. Above all, this is accomplished with stabilising terminal constraints and distinctive terminal cost, both based on an optimal steady-state solution. In addition, a simple method to generate initial guesses for optimisation is introduced. When compared with the performance of a controller based on quasi-static models, our results show notable improvement in velocity tracking while maintaining high fuel economy. Furthermore, our experiments demonstrate that framing energy management as a nonlinear model predictive control provides a flexible and rigorous framework for fast velocity tracking and high energy efficiency. We also compare the results with those of an industrial baseline controller.

A new switched off‐line NMPC approach for nonlinear systems with a switching performance index using an extended modal series method

SummaryThis paper presents a new switched nonlinear model predictive control (NMPC) approach for continuous‐time affine‐input nonlinear systems with a number of different cost functions where switching occurs between them in order to improve the performance. In this approach, the NMPC‐related nonlinear two‐point boundary value problem derived from Pontryagin's maximum principle is solved by the extended modal series method. The resulting suboptimal control law as to each of the cost functions is feasible and has an explicit form. In order to guarantee closed‐loop stability, certain assumptions are considered in the NMPC literature and in the switched systems literature, such as finding an invariant terminal region and a feasible solution for the NMPC and considering a certain average dwell time for switching signals. In this paper, we consider switching among different cost functions using the average dwell‐time approach. Since, in our proposed method, the NMPC problem solution obtained by the extended modal series method is feasible and since the invariance condition for the terminal region is satisfied, the common assumptions for the stability of the switched NMPC can be established. Furthermore, we show that this method guarantees the stability of the entire closed‐loop system in the presence of unknown persistent disturbances. The applicability and effectiveness of the proposed approach are illustrated by two numerical examples.

Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds

In this work we present a whole-body Nonlinear Model Predictive Control approach for Rigid Body Systems subject to contacts. We use a full dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences and timings are not prespecified but optimized by the solver. Yet, thorough numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state of the art by at least one order of magnitude. Hardware experiments in form of periodic and non-periodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability and robustness of the approach.

A multi‐scenario nonlinear model predictive control approach for robust product transitions

Dynamic product transitions are ubiquitous operations in the processing industry. When a first‐principles dynamic model is deployed for real system representation, the calculation of the dynamic optimal trajectory for product transition can be cast as an optimal control problem. A common practice in addressing the solution of optimal product transitions lies in the assumption of free of uncertainty first‐principle models. Ignoring the effect of model uncertainty on product transitions can result in unfeasible dynamic trajectories. In this work, an optimization scenario approach, featuring variable scenario weighting functions, is deployed for assessing the impact of model uncertainty on the control actions such that feasible and optimal transition trajectories are computed featuring minimum deviation from target values. The optimization approach was applied to three nonlinear reaction systems. The results demonstrate that when the variable weighting optimization scenario approach is suitable for approximating model uncertainty, feasible transition trajectories can be calculated at relatively low computational cost (for small or medium scale systems).

Design and construction of a non-linear model predictive controller for building's cooling system

This research aims to optimize a multi-zone Air Handling Unit's (AHU) energy consumption by using a Non-linear Model Predictive Control (NMPC) approach. In this paper, Genetic Algorithm (GA) and Non-linear autoregressive network with exogenous inputs (NARX) have been utilized to design NMPC for a multi-zone AHU. The NMPC problem could be divided into two main sections: internal model and the optimizer. NARX serves as the controller's internal model to predict the building's thermal dynamics. GA is then used to solve the NMPC problem and find the optimal value of the control signals at each time step. The proposed NMPC jointly minimizes energy consumption of the AHU and the deviation from the set-point temperature. Finally, the designed controller was implemented and applied to the mentioned AHU. Also, a data acquisition system has been fabricated to secure training and test data for NARX. Utilizing NARX for modeling system's dynamics resulted in a highly accurate model with an accuracy of 97.71%. The empirical results of the proposed NMPC showed significant reduction in gas and electricity consumption of the AHU. NMPC yielded a 55.1% and 43.7% reduction in electricity and gas consumption of the AHU respectively.

Predictive fault-tolerant control of an all-thruster satellite in 6-DOF motion via neural network model updating

The problem of controlling an all-thruster spacecraft in the coupled translational-rotational motion in presence of actuators fault and/or failure is investigated in this paper. The nonlinear model predictive control approach is used because of its ability to predict the future behavior of the system. The fault/failure of the thrusters changes the mapping between the commanded forces to the thrusters and actual force/torque generated by the thruster system. Thus, the basic six degree-of-freedom kinetic equations are separated from this mapping and a set of neural networks are trained off-line to learn the kinetic equations. Then, two neural networks are attached to these trained networks in order to learn the thruster commands to force/torque mappings on-line. Different off-nominal conditions are modeled so that neural networks can detect any failure and fault, including scale factor and misalignment of thrusters. A simple model of the spacecraft relative motion is used in MPC to decrease the computational burden. However, a precise model by the means of orbit propagation including different types of perturbation is utilized to evaluate the usefulness of the proposed approach in actual conditions. The numerical simulation shows that this method can successfully control the all-thruster spacecraft with ON-OFF thrusters in different combinations of thruster fault and/or failure.

Stability of Gaussian Process Learning Based Output Feedback Model Predictive Control

Abstract We present an output feedback nonlinear model predictive control approach that uses a Gaussian process model for prediction. We show nominal stability assuming that the Gaussian process model is able to represent the real process and establish input-to-state stability assuming a bounded error between the real process and the Gaussian model approximation. These results are achieved using a predictive control formulation without terminal region. The approach is illustrated using a continuous stirred-tank reactor benchmark problem.

Slug handling with a virtual harp based on nonlinear predictive control for a gravity separator

This paper presents a nonlinear model predictive control approach for a three-phase gravity separator model. The aim of the controller is to dampen slug-induced, oscillatory disturbances in the inflow to the gravity separator. This means that, despite the disturbance, the levels of water and oil as well as the pressure should be held at constant operational setpoints. Additionally, a second objective is to dampen the outflows of water, oil and gas and hence keep too large oscillations in flows from downstream equipment. Several constraints are added such as the height of the weir, maximal and minimal allowable levels and pressures as well as constraints on the outflows.

Efficient Train Operation via Shrinking Horizon Parametrized Predictive Control

The problem of driver assistance for the energy-efficient operation of trains is considered. The goal is to control the traction/braking forces applied to the train, while satisfying speed limits and reaching the next station at the prescribed arrival time. Moreover, the control input has to belong to a discrete set of values and/or operating modes, which a human driver has to implement. A nonlinear model predictive control (MPC) approach is proposed, featuring a shrinking horizon and an input-parametrization strategy to retain a continuous optimization problem. Theoretical convergence guarantees are derived, and the approach is tested in realistic simulations.

A Fast NMPC Approach based on Bounded-Variable Nonlinear Least Squares

Abstract In this paper, we present an approach for real-time nonlinear model predictive control (NMPC) of constrained multivariable dynamical systems described by nonlinear difference equations. The NMPC problem is formulated by means of a quadratic penalty function as an always feasible, sparse nonlinear least-squares problem subject to box constraints on the decision variables. This formulation is exploited by the proposed fast solution algorithm, which is based on the Gauss-Newton method and bounded-variable least squares (BVLS). Linear time-invariant and linear time-varying model predictive control based on BVLS are special cases of the proposed NMPC framework. The proposed approach and its benefits are demonstrated through a typical numerical example in simulation.

Handling Structural Plant-model Mismatch using a Model-error Model in the Multi-stage NMPC framework

Nonlinear model predictive control (NMPC) is one of the most promising advanced control approaches for multi-dimensional systems with state and input constraints. Among the several NMPC schemes that were proposed to deal with the uncertainties present in the model, the multi-stage NMPC approach achieves a low degree of conservatism because it incorporates the existence of recourse in the predictions. The future evolution of the state trajectories for different realizations of the uncertainty is modeled as a scenario tree. In this paper, we extend the multi-stage NMPC approach to deal with structural plant-model mismatch in a non-conservative fashion. An uncertainty region around the nominal model is built using a model-error model that consists of stable linear time-invariant dynamics and a static time-variant nonlinear mapping. The scenario tree is built for the nominal and for the extreme realizations of the plant obtained using the nominal model and the model-error model, and a multi-stage decision problem is formulated. We show the advantages of using a model-error model over a previously proposed approach to handle the structural plant model mismatch using multi-stage NMPC for a continuous stirred tank reactor (CSTR) example.