Nonlinear Model Predictive Control of Electrical Submersible Pumps based on Echo State Networks

Employed for artificial lifting in oil well production, Electrical Submersible Pumps (ESP) can be operated with Model Predictive Control (MPC) to drive an optimal production, while ensuring a safe operation and respecting system constraints. Due to the nonlinear dynamics of ESPs, Echo State Networks (ESNs), a recurrent neural network with fast training, are employed for efficient system identification of unknown dynamic systems. Besides the synthesis of highly accurate prediction models, this work contributes by designing two Nonlinear MPC (NMPC) strategies for the control of an ESP-lifted oil well: a standard Single-Shooting NMPC that embeds the ESN model completely, and the Practical Nonlinear Model Predictive Controller (PNMPC) that approximates the NMPC through fast trajectory-linearization of the ESN model. Another contribution is the implementation of an error correction filter to reject disturbances and counter modeling errors in both NMPC strategies. Finally, in computational experiments, both ESN-based NMPC strategies performed well in controlling simulated ESP-lifted oil wells when the model of the plant is unknown. However, PNMPC was more efficient and induced a similar performance to standard NMPC.     

Learning‐based Nonlinear Model Predictive Control to Improve Vision‐based Mobile Robot Path Tracking

This paper presents a Learning‐based Nonlinear Model Predictive Control (LB‐NMPC) algorithm to achieve high‐performance path tracking in challenging off‐road terrain through learning. The LB‐NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modeled as a Gaussian process (GP) as a function of system state, input, and other relevant variables. The GP is updated based on experience collected during previous trials. Localization for the controller is provided by an onboard, vision‐based mapping and navigation system enabling operation in large‐scale, GPS‐denied environments. The paper presents experimental results including over 3 km of travel by three significantly different robot platforms with masses ranging from 50 to 600 kg and at speeds ranging from 0.35 to 1.2 m/s (associated video at http://tiny.cc/RoverLearnsDisturbances ). Planned speeds are generated by a novel experience‐based speed scheduler that balances overall travel time, path‐tracking errors, and localization reliability. The results show that the controller can start from a generic a priori vehicle model and subsequently learn to reduce vehicle‐ and trajectory‐specific path‐tracking errors based on experience.     

A framework for real-time implementation of low-dimensional parameterized NMPC

In this paper, a novel approach is proposed to implement low-dimensional parameterized Nonlinear Model Predictive Control (NMPC) schemes for systems showing fast dynamics. The proposed scheme is based on distributing the reconstruction of the cost function over the real lifetime of the controlled system. The framework is particularly suitable for NMPC formulations that use low dimensional control parametrization. The concrete example of a Planar Vertical Take-Off and Landing (PVTOL) aircraft stabilization problem is used to illustrate the efficiency of the proposed formulation.     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

Adaptive nonlinear model predictive path-following control for a fixed-wing unmanned aerial vehicle

This paper presents an adaptive Nonlinear Model Predictive Control (NMPC) for the path-following control of a fixed-wing unmanned aerial vehicle (UAV). The objective is to minimize the mean and maximum errors between the reference path and the UAV. Navigating in a cluttered environment requires accurate tracking. However, linear controllers cannot provide good tracking performance due to nonlinearities that arise in the system dynamics and physical limitations such as actuator saturation and state constraints. NMPC provides an alternative since it can combine multiple objectives and constraints, which minimize the objective function. However, it is difficult to decide appropriate control horizon since the path-following performance depends on the profile of the path. Therefore, a fixed-horizon NMPC cannot guarantee accurate tracking performance. An adaptive NMPC that varies the control horizon according to the path curvature profile for tight tracking is proposed in this paper. Simulation results show that the proposed adaptive NMPC controller can follow the path more accurately than a conventional, fixed-horizon NMPC.     

一种空间飞行器姿态控制非线性模型的预测控制新算法

空间飞行器的姿态控制受到诸如带时延的非线性动态特性、模型和参数的不确定性等因素的影响 ,其控制相当复杂。传统的控制技术 (如PID控制 )对控制对象的过程模型要求较高 ,且不能解决过程控制中非线性、时变、控制输入的约束性等因素的影响 ,其控制所能达到的性能和效率也远不够满足当前飞行器的控制要求。该文将介绍一种新型的基于控制输入的函数空间最优化的模型预测控制算法 ,称为函数空间模型预测控制 (F -MPC)。该法可用于线性和非线性系统 ,对过程模型要求不高 ,能在控制输入约束条件存在的情况下通过在线优化使系统很好地跟踪期望轨迹 ,并且解决了PID控制所遇到的问题。同时 ,将该算法用于空间飞行器的姿态控制仿真 ,仿真结果表明控制效果很好。     

High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

Explicit stochastic predictive control of combustion plants based on Gaussian process models

Energy production is one of the largest sources of air pollution. A feasible method to reduce the harmful flue gases emissions and to increase the efficiency is to improve the control strategies of the existing thermoelectric power plants. This makes the Nonlinear Model Predictive Control (NMPC) method very suitable for achieving an efficient combustion control. Recently, an explicit approximate approach for stochastic NMPC based on a Gaussian process model was proposed. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation, which is an essential issue in safety-critical applications. This paper considers the application of an explicit approximate approach for stochastic NMPC to the design of an explicit reference tracking NMPC controller for a combustion plant based on its Gaussian process model. The controller brings the air factor (respectively the concentration of oxygen in the flue gases) on its optimal value with every change of the load factor and thus an optimal operation of the combustion plant is achieved.     

Intelligent Multi-Objective Nonlinear Model Predictive Control (iMO-NMPC): Towards the ‘on-line’ optimization of highly complex control problems

The benefits of using the Nonlinear Model Predictive Control (NMPC) for the response optimization of highly complex controlled plants are well known. Nevertheless the complexity and associated high computational cost make its implementation and reliability the focus of the discussion. This paper proposes an Intelligent and Multi-Objective NMPC (iMO-NMPC) scheme where several, and often conflicting, control objectives can be competing simultaneously in the control problem. In the iMO-NMPC, the combination of a Neural Network, a Multi-Objective Genetic Algorithm and a Fuzzy Inference System, help us in the nonlinear search for near-optimal control actions, aiming to fulfil all the specified control objectives simultaneously. The proposed scheme adds an expert stage that can adaptively change the degree of importance (weight) of each control objective according to the state of the plant. Therefore, once the nonlinear multi-objective optimization problem is solved at each sampling time and the non-inferior control solutions belonging to the set of Pareto are obtained, the most appropriate one is selected by using the control objectives weights inferred from the expert stage. Some experimental results showing the iMO-NMPC effectiveness and the details about its implementation over control systems with low sampling times are also presented and discussed in this paper.     

A constrained consensus problem using MPC

This paper presents an MPC (Model Predictive Control) based consensus algorithm which solves a consensus problem in which constraints are imposed on the increment of the state of each agent. After making an artificial consensus trajectory using a previously designed consensus algorithm, the MPC is used to make the agent track the consensus trajectory. Simulation results demonstrate the effectiveness of the proposed algorithm.     

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller.     

Non-Iterative nonlinear model predictive approach applied to the control of helicopters’ group formation

Two geometrical formation schemes that allow the definition of any desired three-dimensional formation mesh for a group of helicopters are presented. Each formation scheme, which defines the leader–follower geometry of the formation mesh, has four parameters. These formation parameters are directly used as the output of decentralized controllers that independently control each helicopter in the group. The decentralized controllers are designed using a non-iterative Nonlinear Model Predictive Control (NMPC) method. The Continuation method is used for solving, in real-time, for future control actions that minimize a NMPC cost function. It is shown by analyzing the number of floating point operations per calculation cycle that the calculation load of the NMPC method for this application is quite manageable for today’s industrial embedded computers. Simulations show that the formation schemes along with the NMPC controller can initialize and keep the formation of a group of helicopters even in the presence of bounded parameter uncertainty and environmental disturbance.     

Flood control of the Demer by using Model Predictive Control

It is shown how Model Predictive Control can be used for flood control of river systems modelled with real data. A linear model for the Demer, a river in Belgium, is derived, which is used inside the optimisation problem solved by the controller. This optimisation problem is formulated such that the controller can be used for set-point and flood control. A Kalman filter is used as a state estimator. Closed loop simulations performed with a full hydrodynamic model of the Demer in combination with historical rainfall data show that the proposed control scheme outperforms the current control strategy.     

Real-time nonlinear MPC and MHE for a large-scale mechatronic application

Progress in optimization algorithms and in computational hardware made deployment of Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) possible to mechatronic applications. This paper aims to assess the computational performance of NMPC and MHE for rotational start-up of Airborne Wind Energy systems. The capabilities offered by an automatic code generation tool are experimentally verified on a real physical system, using a model comprising 27 states and 4 inputs at a sampling frequency of 25 Hz. The results show the feedback times less than 5 ms for the NMPC with more than 1500 variables.     

Trajectory Planning and Control for Airport Snow Sweeping by Autonomous Formations of Ploughs

This article presents a control approach that enables an autonomous operation of fleets of unmanned snow ploughs at large airports. The proposed method is suited for the special demands of tasks of the airport snow shovelling. The robots have to keep a compact formation of variable shapes during moving into the locations of their deployment and for the autonomous sweeping of runways surfaces. These tasks are solved in two independent modes of the airport snow shoveling. The moving and the sweeping modes provide a full-scale solution of the trajectory planning and coordination of vehicles applicable in the specific airport environment. Nevertheless, they are suited for any multi-robot application that requires complex manoeuvres of compact formations in dynamic environment. The approach encapsulates the dynamic trajectory planning and the control of the entire formation into one merged optimization process via a novel Model Predictive Control (MPC) based methodology. The obtained solution of the optimization includes a complete plan for the formation. It respects the overall structure of the workspace and actual control inputs for each vehicle to ensure collision avoidance and coordination of team members. The presented method enables to autonomously design arbitrary manoeuvres, like reverse driving or turning of compact formations of car-like robots, which frequently occur in the airport sweeping application. Examples of such scenarios verifying the performance of the approach are shown in simulations and hardware experiments in this article. Furthermore, the requirements that guarantee a convergence of the group to a desired state are formulated for the formation acting in the sweeping and moving modes.     

A reduced regularization strategy for economic NMPC

Nonlinear Model Predictive Control (NMPC) enables the incorporation of detailed dynamic process models for nonlinear, multivariable control with constraints. This optimization-based framework also leads to on-line dynamic optimization with performance-based and so-called economic objectives. Nevertheless, economic NMPC (eNMPC) still requires careful formulation of the nonlinear programming (NLP) subproblem to guarantee stability. In this study, we derive a novel reduced regularization eNMPC approach with stability guarantees. Compared with full state regularization, the proposed strategy is less conservative and easier to implement. The resulting eNMPC framework is firstly demonstrated on a nonlinear continuous stirred-tank reactor (CSTR) example and a large-scale double distillation system example. Then the proposed strategy is applied to a challenging nonlinear CO₂ capture model, where bubbling fluidized bed models comprise a solid-sorbent post-combustion carbon capture system. Our results indicate the benefits of this improved eNMPC approach over tracking to the setpoint, and better stability over eNMPC without regularization.     

A Novel Discrete-time Nonlinear Model Predictive Control Based on State Space Model

This paper proposes a novel finite dimensional discrete-time Nonlinear Model Predictive Control. This technique is based on discrete-time state-space models, Taylor series expansion for prediction and performance index optimization. Furthermore, the technique extends the concept of the Lie derivative for the discrete time case using Euler backwards method. The performance validation for the discrete-time Nonlinear Model Predictive Control uses the simulation of a single-link flexible joint robot and the inverted pendulum. Comparison of the proposed finite dimensional discrete-time Nonlinear Model Predictive Control technique with Feedback Linearization Control is also discussed. Analytical and numerical results show excellent performances for both, the single-link flexible joint and inverted pendulum controllers using the proposed discrete-time Nonlinear Model Predictive Control technique.     

基于自适应MPC算法的轨迹跟踪控制研究

为了保证智能车辆在低附着且变速条件下跟踪控制的精确性和稳定性,提出一种基于自适应模型预测控制（MPC）的轨迹跟踪控制算法。针对低附着条件下轨迹跟踪存在行驶稳定性较差的问题,对车辆动力学模型添加侧偏角软约束,分别设计有无添加侧偏角约束的MPC控制器。仿真结果表明,添加侧偏角约束后MPC控制器性能更优,车辆行驶稳定性得到有效提高。在此基础上,又提出了一种自适应的轨迹跟踪控制策略,能够根据车辆速度的变化,实时产生预测时域[(Hp)],分别设计自适应的MPC控制器与4组定值[Hp]的MPC控制器。仿真结果表明,基于自适应模型预测控制的轨迹跟踪控制算法在提高低附着且变速条件下智能车辆轨迹跟踪控制的精度和稳定性方面具有一定的有效性和先进性。     

Planar bipedal locomotion control based on state discretization

In this paper, a new control method for a planar bipedal robot, which we call Graph-based Model Predictive Control, is proposed. This method makes use of a directed graph constructed on the state space of the robot. The vertices of the directed graph are called waypoints, and they serve as intermediate target states to compose complex motions of the robot. By simply tracing the directed edges of the graph, one can achieve Model Predictive Control over the waypoint set. Such a directed graph is pre-designed and stored into the controller’s memory to significantly reduce the computational effort required in real time. In addition, by constructing multiple directed graphs based on different objective functions, one can design multiple motions and switching trajectories among them in a uniform way. The proposed method is applied to variable-speed walking control of a bipedal walker on a two-dimensional plane, and its effectiveness is verified by numerical simulations.     

一种基于T-S模型的模糊预测控制

提出了一种基于T-S模型的模糊预测控制策略。T-S模糊模型用来描述对象的非线性动态特性,通过当前的工况参数实时在线的修正每一时刻的阶跃响应模型参数,将模糊模型作为常规线性预测控制DMC方法的预测模型,从而把T-S模型对复杂的非线性系统的良好描述特性和预测控制的滚动优化算法相结合,来实现利用常规线性预测控制策略对非线性系统的有效控制,有效地解决了复杂工业过程的强非线性问题。pH中和过程的仿真结果表明其性能明显优于传统的PID控制器。