Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

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

Nonlinear model predictive control(NMPC)scheme is an effective method of multi-objective optimization control in complex industrial systems.In this paper,a NMPC scheme for the wet limestone flue gas desulphurization(WFGD)system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme.At first,a mathematical model of the FGD process is deduced which is suitable for NMPC structure.To equipoise the model’s accuracy and conciseness,the wet limestone FGD system is separated into several modules.Based on the conservation laws,a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design.Then,by addressing economic objectives directly into the NMPC scheme,the NMPC controller can minimize economic cost and track the set-point simultaneously.The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province,China.The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time.In the meantime,the control scheme satisfies the multiobjective control requirements under complex operation conditions(e.g.,boiler load fluctuation and set point variation).The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.

Pre-compensation of Friction for CNC Machine Tools through Constructing a Nonlinear Model Predictive Scheme

Nonlinear friction is a dominant factor afecting the control accuracy of CNC machine tools.This paper proposes a friction pre-compensation method for CNC machine tools through constructing a nonlinear model predictive scheme.The nonlinear friction-induced tracking error is frstly modeled and then utilized to establish the nonlinear model predictive scheme,which is subsequently used to optimize the compensation signal by treating the friction-induced tracking error as the optimization objective.During the optimization procedure,the derivative of compensation signal is constrained to avoid vibration of machine tools.In contrast to other existing approaches,the proposed method only needs the parameters of Stribeck friction model and an additional tuning parameter,while fnely identifying the parameters related to the pre-sliding phenomenon is not required.As a result,it greatly facilitates the practical applicability.Both air cutting and real cutting experiments conducted on an in-house developed open-architecture CNC machine tool prove that the proposed method can reduce the tracking errors by more than 56%,and reduce the contour errors by more than 50%.

Nonlinear model predictive control with relevance vector regression and particle swarm optimization

In this paper, a nonlinear model predictive control strategy which utilizes a probabilistic sparse kernel learning technique called relevance vector regression （RVR） and particle swarm optimization with controllable random exploration velocity （PSO-CREV） is applied to a catalytic continuous stirred tank reactor （CSTR） process. An accurate reliable nonlinear model is first identified by RVR with a radial basis function （RBF） kernel and then the optimization of control sequence is speeded up by PSO-CREV. Additional stochastic behavior in PSO-CREV is omitted for faster convergence of nonlinear optimization. An improved system performance is guaranteed by an accurate sparse predictive model and an efficient and fast optimization algorithm. To compare the performance, model predictive control （MPC） using a deterministic sparse kernel learning technique called Least squares support vector machines （LS-SVM） regression is done on a CSTR. Relevance vector regression shows improved tracking performance with very less computation time which is much essential for real time control.

Wiener model identification and nonlinear model predictive control of a pH neutralization process based on Laguerre filters and least squares support vector machines

This paper deals with Wiener model based predictive control of a pH neutralization process.The dynamic linear block of the Wiener model is parameterized using Laguerre filters while the nonlinear block is constructed using least squares support vector machines (LSSVM).Input-output data from the first principle model of the pH neutralization process are used for the Wiener model identification.Simulation results show that the proposed Wiener model has higher prediction accuracy than Laguerre-support vector regression (SVR) Wiener models,Laguerre-polynomial Wiener models,and linear Laguerre models.The identified Wiener model is used here for nonlinear model predictive control (NMPC) of the pH neutralization process.The set-point tracking performance of the proposed NMPC is compared with those of the Laguerre-SVR Wiener model based NMPC,Laguerre-polynomial Wiener model based NMPC,and linear model predictive control (LMPC).Validation results show that the proposed NMPC outperforms the other three controllers.

Nonlinear Model Predictive Control-Based Guidance Algorithm for Quadrotor Trajectory Tracking with Obstacle Avoidance

This paper studies a novel trajectory tracking guidance law for a quadrotor unmanned aerial vehicle(UAV)with obstacle avoidance based on nonlinear model predictive control(NMPC)scheme.By augmenting a reference position trajectory to a reference dynamical system,the authors formulate the tracking problem as a standard NMPC design problem to generate constrained reference velocity commands for autopilots.However,concerning the closed-loop stability,it is difficult to find a local static state feedback to construct the terminal constraint in the design of NMPC-based guidance law.In order to circumvent this issue,the authors introduce a contraction constraint as a stability constraint,which borrows the ideas from the Lyapunov’s direct method and the backstepping technique.To achieve the obstacle avoidance extension,the authors impose a well-designed potential field function-based penalty term on the performance index.Considering the practical application,the heavy computational burden caused by solving the NMPC optimization problem online is alleviated by using the dynamical adjustment of the prediction horizon for the real-time control.Finally,extensive simulations and the real experiment are given to demonstrate the effectiveness of the proposed NMPC scheme.

A double-layered nonlinear model predictive control based control algorithm for local trajectory planning for automated trucks under uncertain road adhesion coefficient conditions

We present a double-layered control algorithm to plan the local trajectory for automated trucks equipped with four hub motors. The main layer of the proposed control algorithm consists of a main layer nonlinear model predictive control(MLN-MPC) controller and a secondary layer nonlinear MPC(SLN-MPC) controller. The MLN-MPC controller is applied to plan a dynamically feasible trajectory, and the SLN-MPC controller is designed to limit the longitudinal slip of wheels within a stable zone to avoid the tire excessively slipping during traction. Overall, this is a closed-loop control system. Under the off-line co-simulation environments of AMESim, Simulink, dSPACE, and TruckSim, a dynamically feasible trajectory with collision avoidance operation can be generated using the proposed method, and the longitudinal wheel slip can be constrained within a stable zone so that the driving safety of the truck can be ensured under uncertain road surface conditions. In addition, the stability and robustness of the method are verified by adding a driver model to evaluate the application in the real world. Furthermore, simulation results show that there is lower computational cost compared with the conventional PID-based control method.

A Quantum-behaved Pigeon-Inspired Optimization approach to Explicit Nonlinear Model Predictive Controller for quadrotor

Purpose–The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller(ENMPC)by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization(QPIO).Design/methodology/approach–The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory.Since the ENMPC has high demand for the state equation,the trajectory needed to be differentiated many times.When the trajectory is complicate or discontinuous,QPIO is proposed to linearize the trajectory.Then the linearized trajectory will be used in the ENMPC.Findings–Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory.Comparing with the equidistant linear interpolation,the linear interpolation error will be smaller.Practical implications–Small-sized quadrotors were adopted in this research to simplify the model.The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.Originality/value–Traditionally,the quadrotor model was usually linearized in the research.In this paper,the quadrotormodel waskept nonlinear and the trajectorywill be linearizedinstead.Unequaldistance sample points were utilized to linearize the trajectory.In this way,the authors can get a smaller interpolation error.This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.

GA-Based Model Predictive Control of Semi-Active Landing Gear

Semi-active landing gear can provide good performance of both landing impact and taxi situation, and has the ability for adapting to various ground conditions and operational conditions. A kind of Nonlinear Model Predictive Control algorithm （NMPC） for semi-active landing gears is developed in this paper. The NMPC algorithm uses Genetic Algorithm （GA） as the optimization technique and chooses damping performance of landing gear at touch down to be the optimization object. The valve＇s rate and magnitude limitations are also considered in the controller＇s design. A simulation model is built for the semi-active landing gear＇s damping process at touchdown. Drop tests are carried out on an experimental passive landing gear systerm to validate the parameters of the simulation model. The result of numerical simulation shows that the isolation of impact load at touchdown can be significantly improved compared to other control algorithms. The strongly nonlinear dynamics of semi-active landing gear coupled with control valve＇s rate and magnitude limitations are handled well with the proposed controller.

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes （VSCMGs） with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account, a feedback control law is designed for the system based on a method of nonlinear model predictive control （NMPC）. The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.

An integrated approach for machine-learning-based system identification of dynamical systems under control:application towards the model predictive control of a highly nonlinear reactor system

Advanced model-based control strategies,e.g.,model predictive control,can offer superior control of key process variables for multiple-input multiple-output systems.The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization.This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control.To showcase this approach,five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system.This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges.These controllers also had reasonable per-iteration times of ca.0.1 s.This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which,in the face of process uncertainties or modelling limitations,allow rapid and stable control over wider operating ranges.

Neural network-based model predictive control with fuzzy-SQP optimization for direct thrust control of turbofan engine

A nonlinear model predictive control method based on fuzzy-Sequential Quadratic Programming(SQP)for direct thrust control is proposed in this paper for the sake of improving the accuracy of thrust control.The designed control system includes four parts,namely a predictive model,rolling optimization,online correction,and feedback correction.Considering the strong nonlinearity of engine,a predictive model is established by Back Propagation(BP)neural network for the entire flight envelope,whose input and output are determined with random forest algorithm and actual situation analysis.Rolling optimization typically uses SQP as the optimization algorithm,but SQP algorithm is easy to trap into local optimization.Therefore,the fuzzy-SQP algorithm is proposed to prevent this disadvantage using fuzzy algorithm to determine the initial value of SQP.In addition to the traditional three parts of model predictive control,an online correction module is added to improve the predictive accuracy of the predictive model in the predictive time domain.Simulation results show that the BP predictive model can reach a certain degree of predictive accuracy,and the proposed control system can achieve good tracking performance with the limited parameters within the safe range。

Real-Time nonlinear predictive controller design for drive-by-wire vehicle lateral stability with dynamic boundary conditions

Due to flexible drive-by-wire technology,vehicle stability control can improve handling and lateral stability under extreme conditions.However,this technology can also increase the probability of random transmission delay.This paper proposes a nonlinear model predictive control(NMPC)strategy to improve vehicle stability and compensate for the random time delay.First,by combining the nonlinear dynamic characteristics and driver behavior,we obtain a stable region of the yaw rate and the sideslip angle under complex driving conditions.Second,an NMPC controller is designed to track the reference values in the identified stable region to improve the handling and lateral stability.Finally,the actuator receives the optimized control sequence and compensates for the random time delay of the transmission channel.CarSim/Simulink simulation and hardware-in-the-loop experiment results show that the proposed controller with dynamic boundary conditions can better track the expected value of the yaw rate and suppress the sideslip angle under low adhesion road conditions.

Real‑Time Predictive Control of Path Following to Stabilize Autonomous Electric Vehicles Under Extreme Drive Conditions

A novel real-time predictive control strategy is proposed for path following(PF)and vehicle stability of autonomous electric vehicles under extreme drive conditions.The investigated vehicle configuration is a distributed drive electric vehicle,which allows to independently control the torques of each in-wheel motor(IWM)for superior stability,but bringing control com-plexities.The control-oriented model is established by the Magic Formula tire function and the single-track vehicle model.For PF and direct yaw moment control,the nonlinear model predictive control(NMPC)strategy is developed to minimize PF tracking error and stabilize vehicle,outputting front tires’lateral force and external yaw moment.To mitigate the calcu-lation burdens,the continuation/general minimal residual algorithm is proposed for real-time optimization in NMPC.The relaxation function method is adopted to handle the inequality constraints.To prevent vehicle instability and improve steering capacity,the lateral velocity differential of the vehicle is considered in phase plane analysis,and the novel stable bounds of lateral forces are developed and online applied in the proposed NMPC controller.Additionally,the Lyapunov-based constraint is proposed to guarantee the closed-loop stability for the PF issue,and sufficient conditions regarding recursive feasibility and closed-loop stability are provided analytically.The target lateral force is transformed as front steering angle command by the inversive tire model,and the external yaw moment and total traction torque are distributed as the torque commands of IWMs by optimization.The validations prove the effectiveness of the proposed strategy in improved steering capacity,desirable PF effects,vehicle stabilization,and real-time applicability.

Modeling, simulation and control of a twin-inverted pendulum on a moving cart

In this paper,a mathematical model of a twin-inverted pendulum on a moving cart has been derived.This is done using the Lagrange–Euler method and,hence,a highly nonlinear mathematical model is resulted from this derivation.These nonlinear and unstable dynamics are written in a simple matrix form.For this challenging system,we use two types of efficient control approaches to treat the control problem of the twin inverted pendulum,namely,linear quadratic regulator(LQR)and nonlinear model predictive control(NMPC).Simulations with several scenarios are also presented to demonstrate the control performances and the model validity.

Pneumatic pressure control based on improved NMPC and its application to aeroengine surge simulation

In the semi-physical simulation of aeroengines,using the pneumatic pressure servo control technology to provide realistic pneumatic excitation to the sensors and electronic controller can improve the confidence of the simulation and reduce the test cost and risk.However,the existing methods could not satisfy the precise simulation of large-amplitude and high-frequency pulsating pressure during aeroengine surge.In this paper,a pneumatic pressure control system with asymmetric groups of the High-Speed on–off Valve(HSV)is designed,and an Improved Nonlinear Model Predictive Control(INMPC)method is proposed.First,the volumetric flow characteristics of HSV are tested and analyzed with Pulse Width Modulation(PWM)signal input.Then,a simplified HSV model with the volume flow characteristic correction is developed.Based on these,an integrated model for the whole system is further established and used as the prediction model in INMPC.To improve the computational speed of the rolling optimization process,the mapping scheme from control signal to PWM duty cycle of HSVs and the objective function with exterior penalty function are designed.Finally,the random step,sinusoidal and real engine surge data are set as the reference pressure in multiple comparative experiments to verify the effectiveness of the pressure tracking system.