Nonlinear Predictive Control Scheme Research Articles

Virtual unmodeled dynamic and data-driven nonlinear robust predictive control

This study presents a novel approach for controlling an industrial process that exhibits uncertainty and significant nonlinear features. The proposed method utilizes a virtual unmodeled dynamic and data-driven nonlinear robust predictive control strategy. The representation of a controlled object involves a composite state space model that combines both linear and high-order nonlinear elements. Moreover, a robust model predictive controller is developed using the linear component. In addition, the notion of one-step optimal feedforward is used in combination with a compensating controller to handle the high-order nonlinear factor specifically. Subsequently, a compensation controller with incremental characteristics is developed for a modified version of the high-order nonlinear term. Furthermore, the stability conditions of the closed-loop system are derived, and an analysis is conducted on the stability and convergence of the proposed approach. The TTS20 three-capacity water tank was utilized in both simulations and practical scenarios. The study demonstrated that the suggested approach successfully reduces system output variations and enhances overall performance in response to unpredictable changes in the process’s dynamic features.

Predictive trajectory tracking control for the USV in networked environments with communication constraints

The trajectory tracking control problem of under-actuated unmanned surface vessels (USVs) suffering from communication constraints (network delay, packet loss, packet disorder) as well as external environment disturbance is investigated in this paper. To solve the aforementioned trajectory control problem, a nonlinear networked predictive control strategy based on the discrete sliding mode framework is proposed. Initially, using the forward Euler discretization method, a novel discrete virtual velocity control law is designed to transform trajectory tracking control into virtual velocity tracking control. Then, a sliding mode controller is suggested to suppress external disturbance of the USV. In addition, a networked sliding mode predictive control (NSMPC) scheme is proffered to guarantee active compensation of the communication constraints and stability of the trajectory tracking system simultaneously. Afterward, a theoretical analysis is given to show that the closed-loop system is uniformly bounded stable after the introduction of the digital network. Finally, extensive comparative simulation examples are provided to demonstrate the effectiveness of the proposed control strategy.

Predictive control of reactor network model using machine learning for hydrogen-rich gas and biochar poly-generation by biomass waste gasification in supercritical water

Supercritical water gasification (SCWG) technology can convert biomass into hydrogen rich gas and biochar. Fluidized bed reactor is promising for the industrialization of this technology, and the reactor dynamic performance study is of great significance for its scaling up. However, current simulation studies mainly focus on steady-state analysis using Computational Fluid Dynamics (CFD) software, it is difficult to conduct dynamic study due to its high computational costs. To this end, a reactor network model (RNM) that accounts for the flow, heat transfer, and kinetic dynamics for fluidized bed reactor is firstly developed based on the partitioning theory, which can reduce the computation time of dynamic simulation from several days to seconds. Additionally, extensive open-loop simulations of the RNM are carried out to generate the dataset for the development of a recurrent neural network (RNN) model. Additionally, current studies mainly focus on open-loop simulation, closed loop optimization is absent. To this end, a framework for building a machine learning (ML) model and a ML-based nonlinear predictive control scheme is developed. Model predictive control (MPC) schemes based on the RNN model is used to optimize the SCWG process to achieve multiple objectives, such as maximizing hydrogen yield and carbon yield. The open loop simulation results demonstrate that H2 yield decreases from 0.00022 to 0.0002 kg s−1 with temperature reducing from 700 to 600 °C. To increase H2 yield to the setpoint, MPC increases temperature and mass flowrate to 708 °C and 417.57 kg h−1. Additionally, MPC increases carbon yield and minimizing CO2 yield by decreasing temperature to 475 °C and increasing mass flowrate to 407.38 kg h−1.

Computationally Efficient Stability-Based Nonlinear Model Predictive Control Design for Quadrotor Aerial Vehicles

This article presents the design of a stability-guaranteed nonlinear model predictive controller for quadrotor-type microaerial vehicles to operate robustly on fast trajectories. The basic controller structure operates without having to use terminal conditions in the optimization problem. As a result, the controller is computationally less demanding and provides more stable closed-loop performance than traditional nonlinear predictive control schemes. This article presents a detailed stability analysis without terminal costs or terminal constraints and proves the asymptotic stability and necessary conditions for the recursive feasibility of the system. This article derives the growth-bound sequence that enables obtaining the shortest possible prediction horizon for stability. The proposed analysis provides the necessary conditions to implement the controller while using the shortest stabilizing prediction horizon compared to major traditional predictive control schemes reported in the literature. This particular feature enables the proposed controller to perform fast optimization and, hence, the capability to implement fast trajectories using feedback regularization. In order to demonstrate the validity of this new proposed control scheme, first, several MATLAB simulations are conducted to demonstrate the improved performance of the controller especially when the quadrotor vehicle follows fast trajectories. Real-time lab experiments are also conducted to validate the performance of the proposed scheme for point stabilization (hovering) and trajectory tracking problems. The results show that the proposed scheme can stabilize the system with a relatively short prediction horizon, a fast convergence rate, and a small tracking error.

Data-driven nonlinear predictive control for feedback linearizable systems

We present a data-driven nonlinear predictive control approach for the class of discrete-time multi-input multi-output feedback linearizable nonlinear systems. The scheme uses a non-parametric predictive model based only on input and noisy output data along with a set of basis functions that approximate the unknown nonlinearities. Despite the noisy output data as well as the mismatch caused by the use of basis functions, we show that the proposed multi-step robust data-driven nonlinear predictive control scheme is recursively feasible and renders the closed-loop system practically exponentially stable. We illustrate our results on a model of a fully-actuated double inverted pendulum.

Design of High-Dynamic PMSM Servo Drive Using Nonlinear Predictive Controller with Harmonic Disturbance Observer

The high-dynamic permanent magnet (PM) motor servo system with high-bandwidth is the core equipment for industrial production, and the control bandwidth is also an important indexes to evaluate the performance of the servo system. The non-cascaded direct predictive speed control is an appropriate scheme to optimize the dynamic performance of the PM motor servo system. However, the high bandwidth of the non-cascaded control structure results in poor anti-interference ability, and it cannot effectively deal with the coupling relationship between current and speed, leading to poor control performance in the current limit region. Regarding the above problems, a nonlinear predictive speed control strategy combined with harmonic disturbance observer is proposed. In the proposed strategy, the disturbances of the servo system are separated from the mathematical model according to the nonlinear modeling theory, and the traditional disturbance observer is modified to estimate the harmonics. A nonlinear control law with strong disturbance suppression ability was designed. Furthermore, a complete current and speed prediction mechanism was introduced into the algorithm, in which the proportional differential (PD) controller is employed as the connection medium between the reference current and speed to solve the coupling problem of the non-cascaded control structure.

Cooperative Control for Dual Permanent Magnet Motor System with Unified Nonlinear Predictive Control

In order to improve the position tracking precision of dual permanent magnet synchronous motor (PMSM) systems, a unified nonlinear predictive control (UNPC) strategy based on the unified modeling of two PMSM systems is proposed in this paper. Firstly, establishing a unified nonlinear model of the dual-PMSM system, which contains uncertain disturbances caused by parameters mismatch and external load changes. Then, the position contour error and tracking errors are regarded as the performance index inserted into the cost function, and the single-loop controller is obtained by optimizing the cost function. Meanwhile, the nonlinear disturbance observer is designed to estimate the uncertain disturbances, which is used for feed-forward compensation control. Finally, the proposed strategy is experimentally validated on two 2.3 kW permanent magnet synchronous motors, and the experimental results show that effectiveness and feasibility of proposed strategy.

A parametrized nonlinear predictive control strategy for relaxing COVID-19 social distancing measures in Brazil

The SARS-CoV-2 virus was first registered in Brazil by the end of February 2020. Since then, the country counts over 150000 deaths due to COVID-19 and faces a profound social and economic crisis; there is also an ongoing health catastrophe, with the majority of hospital beds in many Brazilian cities currently occupied with COVID-19 patients. Thus, a Nonlinear Model Predictive Control (NMPC) scheme used to plan appropriate social distancing measures (and relaxations) in order to mitigate the effects of this pandemic is formulated in this paper. The strategy is designed upon an adapted data-driven Susceptible–Infected–Recovered–Deceased (SIRD) model, which includes time-varying auto-regressive immunological parameters. A novel identification procedure is proposed, composed of analytical regressions, Least-Squares optimization and auto-regressive model fits. The adapted SIRD model is validated with real data and able to adequately represent the contagion curves over large forecast horizons. The NMPC strategy is designed to generate piecewise constant quarantine guidelines, which can be reassessed (relaxed/strengthened) each week. Simulation results show that the proposed NMPC technique is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to a “no-control” condition, the number of deaths could be reduced in up to 30% if the proposed NMPC coordinated health policy measures are enacted.

Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

Experimental Evaluation of Parameterized Nonlinear MPC Applied to PEM Fuel Cell

This paper proposes a parameterized nonlinear model-based predictive control (NMPC) strategy to tackle the oxygen excess ratio regulation challenge of a proton exchange membrane fuel cell. In practice, the most challenging part regarding NMPC strategies remains the on-line implementation. In fact, NMPC strategies, at least in their basic form, involve heavy computation to solve the optimization problem. In this work, a specific parameterization of control actions has been designed to address this limitation and achieve on-line implementation. To assess the effectiveness and relevance of the proposed strategy, the controller has been implemented on-line, experimentally validated on a real fuel cell and compared to the built-in controller. Performance of the parameterized NMPC controller in terms of setpoint tracking accuracy, disturbances rejection and computational cost, have tested under several control scenarios. Experimental results have shown the excellent tracking capability, disturbances rejection ability and low computational cost of the NMPC controller, regardless of the operating conditions. Moreover, compared to the built-in controller the proposed strategy has demonstrated better disturbances rejection capability. Overall, the proposed parameterized NMPC controller appears as an excellent candidate to address the oxygen excess ratio regulation issue.

An Improved Nonlinear Predictive Control Strategy Enhanced by Fractional Order Extremum Seeking Control of the Antilock Braking System of a Vehicle

Extremum seeking control can search the optimal slip rate of the antilock braking system of a vehicle through a high-frequency sinusoidal excitation signal. However, because of the bandwidth limitation of the braking actuator, the search speed of the optimal slip rate decreases and the stability of the extremum seeking control system becomes worse. To search and control the optimal slip rate, an improved nonlinear predictive control strategy enhanced by fractional order extremum seeking control is proposed for the vehicle antilock braking system. First, the nonlinear dynamic model of the braking system is established. Then, nonlinear prediction control is designed with the prediction of the slip rate response based on the nonlinear model to achieve slip rate control. Using fractional order calculus, a fractional extremum seeking controller is proposed to search for the optimal slip rate. Nonlinear predictive control integrated with fractional extremum seeking control is proposed to achieve the function of vehicle antilock braking. Finally, the effectiveness of the proposed method is verified by simulating the vehicle antilock braking system under different road conditions. The result shows that by considering the actuator available bandwidth, the proposed fractional order extremum seeking control can improve the search speed of the optimal slip rate compared with traditional integer order extremum seeking control. The proposed integrated controller achieves wheel slip rate optimal control regardless of the road conditions.

A state estimator–based nonlinear predictive control for a fractional-order Francis hydraulic turbine governing system

A nonlinear predictive control scheme with a state estimator for a fractional-order hydraulic turbine governing system is studied in this article. First, a more practical fractional-order model of the hydraulic turbine governing system is introduced. Second, according to the Grünwald–Letnikov definition of fractional calculus, the fractional-order hydraulic turbine governing system is transformed into a nonlinear discrete model. Third, based on the Takagi–Sugeno fuzzy theory, a fuzzy prediction model of the fractional-order hydraulic turbine governing system is presented. Furthermore, a state estimator–based nonlinear predictive control scheme is proposed for the fractional-order hydraulic turbine governing system, and the controller gain can be obtained by solving a linear matrix inequality. Finally, experimental results show that the proposed state estimator–based nonlinear predictive control could effectively restrain the oscillation of the fractional-order hydraulic turbine governing system under various working conditions.

Braking/steering coordination control for in-wheel motor drive electric vehicles based on nonlinear model predictive control

Braking and steering are common maneuvers performed by drivers during driving. This paper presents a hierarchy control strategy to coordinate the braking and steering performance for in-wheel motor drive electric vehicles (IWMD EVs). A particle swarm optimization-based nonlinear predictive control (PSO-NMPC) scheme is proposed to calculate the required longitudinal force, lateral force and yaw moment of the vehicle in the upper controller. In the lower controller, the PSO algorithm is again utilized to realize the required forces and yaw moment through optimal torque allocation and brake actuator regulation while maintaining vehicle stability and maximizing the regenerative braking recovery. A fault-tolerance mechanism is also incorporated to enhance the robustness of the proposed method. Finally, the effectiveness of the proposed scheme is examined under various braking execution scenarios through the Carmaker-Simulink co-simulation. The results show that the proposed scheme outperforms other state-of-the-art methods in all-round aspects.

Oil production increase in unstable gas lift systems through nonlinear model predictive control

Oil production employing gas lift techniques enable the production of no natural flow wells and supply the energy lost in the reservoir caused by the field depletion, keeping the production in brown fields feasible. The multiphase flow conditions and the long pipes used to transport the fluids from the reservoir to the surface facilities, especially in deep and ultra-deepwater cases, may create unstable flow situations. Several publications in process control have discussed this problem since the 1980s, but the potential multivariable actions on the choke valve and gas lift flow have not been explored so far. In this paper the operating oil production system is treated through a nonlinear predictive control strategy. The strategy evaluation in a rigorous model (OLGA) shows the association between predictive capability and the integrated actuation in the manipulated variables results in an oil production increase and a partial or entire suppression of the instabilities in the multiphase flow. Furthermore, the rate of acting required on the valves is lower in the multivariable approach, allowing the use of slow choke valves as a final control element.

Application of nonlinear multivariable model predictive control to transient operation of a gas turbine and NOX emissions reduction

This work aims to apply a multivariable nonlinear model-based predictive control strategy (MPC) to avoid unsafe or inappropriate operation of gas turbines, while reducing NOx emissions. In this context, the control variables are the compressor speed and the temperature after the turbine. The controller maintains the speed proportional to the grid frequency during load changes. Additionally, in cases where the turbine is installed in a combined heat and power cycle, the discharge temperature must follow a reference, to ensure the quality of the steam generated. The control is achieved by manipulating the fuel flow in the combustion chamber and the variable inlet guide vanes of the compressor. The nonlinear dynamic behavior of an industrial gas turbine is modeled using a first principle process simulator, which solves the mass, energy and momentum conservation equations, together with an equation of state. Furthermore, pollutant emissions are minimized as part of the process, through an optimization procedure. The optimization problem is solved through the implementation of three different evolutionary algorithms and one direct search method. The proposed control strategy is successfully applied to a gas turbine in load rejection scenarios, and the optimization fulfills its goal by reducing nitrogen oxides emissions.

A non-minimum phase robust nonlinear neuro-wavelet predictive control strategy for a quadruple tank process

In process industries model-plant mismatch is a significant problem. Quadruple tank process (QTP) can be configured both in minimum phase and non-minimum phase (NMP). However, in NMP, the control of QTP poses a challenge. This paper addresses that and presents a novel robust wavelet based non-minimum phase control (NMPC) strategy for the challenging QTP using genetic algorithm to find the optimised value of the manipulated variables in NMPC at every sampling time. The QTP is modelled based on wavelet neural network. The simulation results indicate that significant improvements have been achieved both in modelling and control strategies for a QTP system compare to conventional approaches such as the Levenberg-Marquardt.

A non-minimum phase robust nonlinear neuro-wavelet predictive control strategy for a quadruple tank process

In process industries model-plant mismatch is a significant problem. Quadruple tank process (QTP) can be configured both in minimum phase and non-minimum phase (NMP). However, in NMP, the control of QTP poses a challenge. This paper addresses that and presents a novel robust wavelet based non-minimum phase control (NMPC) strategy for the challenging QTP using genetic algorithm to find the optimised value of the manipulated variables in NMPC at every sampling time. The QTP is modelled based on wavelet neural network. The simulation results indicate that significant improvements have been achieved both in modelling and control strategies for a QTP system compare to conventional approaches such as the Levenberg-Marquardt.

Design of Nonlinear Predictive Control for Pneumatic Muscle Actuator Based on Echo State Gaussian Process

Recently, the application of Pneumatic Muscle Actuators (PMAs) for driving rehabilitation robots has become a matter of great concern. A traditional control algorithm, such as PID, cannot achieve satisfactory high-precision performance in trajectory tracking problem for PMAs, due to PMAs’ features of nonlinear effects, slow response time, time-varying parameters. In this study we proposed a nonlinear predictive control strategy SNN-ESGP, which is comprised of a novel model called echo state Gaussian process (ESGP) that is suitable for modeling nonlinear unknown systems as well as measuring their uncertainties, and a single neural network (SNN) serves as the controller of the system. To analyze the system convergence, we utilize the gradient descent algorithm and deduce the iterative rules of the weights of SNN. The stability of the closed-loop system is analyzed by using Lyapunov theorem. Finally, studies of physical experiments illustrate the validity of the control strategy with high-precision trajectory performance.

Evaluation of Nonlinear Model-Based Predictive Control Approaches Using Derivative-Free Optimization and FCC Neural Networks

Nonlinear control methods have been researched with the objective of improving performance of control loop systems. Among such control methods, nonlinear model-based predictive control (NMPC) strategies present significant importance, mainly due to explicit performance optimization and constraint handling. NMPC depends on a representative nonlinear model of the process to be controlled and an adequate optimization method. This work focuses on these two aspects. Simulation tests with a wastewater treatment process model are presented, to evaluate the use of two optimization methods, differential evolution and bound optimization by quadratic approximation (BOBYQA), under different conditions. Experimental results using BOBYQA and a fully connected cascade artificial neural network in a pressure process are presented, showing a performance improvement comparing to a linear model predictive controller.

Active and reactive power control via currents of a rotor’s d and q components with nonlinear predictive control strategy in a doubly fed induction generator based on wind power system

Wind energy today, has attracted widespread interest from among a variety of sources of renewable energy in the world. Owing to the increasing demand for production of electrical energy for electricity networks by using wind power, it is essential that wind power plants are actively incorporated in the network’s performance using an appropriate control system. In general, these wind power plants consist of various types of wind turbines and generators, one of them being a doubly fed induction generator (DFIG). Strict and total control of DFIG is necessary for maintaining a high level of efficiency in utilizing the advantages and benefits of a modern wind plant. To achieve this aim, using the linear controllers is a difficult method because the wind plants involve some uncertainties. Nevertheless, there exists an unstable condition which may reduce the DFIG system’s performance. In this research, a predictive control has been proposed for power control in order to overcome these problems. Control is established by optimizing a Cost Function considering the reality of the tracking factors. The prediction has been done on the basis of a DFIG model. Finally, results of the simulations carried out proved the performance of the controller. Article history: