Robust Model Predictive Control for the Beam-Pumping Unit Dynamic Liquid Level Stabilization

This paper addresses a computationally efficient robust tube-based model predictive control (RTBMPC) strategy of linear systems in the presence of bounded disturbance. In the RTBMPC strategy, a nominal system is introduced by ignoring the disturbances of uncertain system, and then the uncertain system will be controlled in a robust manner through its nominal system as well as an additional feedback term which rejects a bounded additive disturbance. In this paper, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function and simplification of driving the stability theory. On the other hand, RTBMPC strategy solves optimization problem for nominal system which ignores the disturbances. Since in the absence of disturbances, the state measured at the following sample will be the same as the one predicted by model, a variable prediction horizon is suggested to reduce the computational burden. In addition, new constraints are introduced to prove the recursive feasibility, local and asymptotic stability. The constrained sampled double integrator is presented to illustrate the effectiveness of the proposed RTBMPC.

Dynamic Output Disturbance Models for Robust Constraint Satisfaction

This paper presents a method to design a predictive controller for a single Inverted Pendulum (SIP) system. The design goal is to balance the pendulum in the inverted position in the presence of parameter variations and measurement white noise Using linearization technique, the model of SIP system is transformed to a linear polytopic system. Since we need to estimation of states, a new robust model predictive control (RMPC) strategy is developed for this system with considering white measurement noise. Simulation results are presented to show the robustness of the closed-loop system against parameter variations and measurement white noise.

This paper presents a method to design a predictive controller for a Rotational Inverted Pendulum (RIP) system. The design goal is to balance the pendulum in the inverted position. After linearization, the model of RIP system is transformed to a linear polytopic system with bounded disturbances and a new robust model predictive control (RMPC) strategy is developed for this system. Simulation results are presented to show the robustness of the closed-loop system against parameter variations and disturbances. The proposed method can be considered as a promising way for control of various similar nonlinear systems.

Constant-air-volume (CAV) air-conditioning systems consist mainly of two local processes: an air-handling process and a room temperature process. A robust model predictive control (RMPC) strategy was developed for CAV air-conditioning systems, which adopted two uncertain first-order plus time-delay models to describe the dynamics of the local processes and used a linear matrix inequality (LMI)-based optimisation technique to optimise the control law. This paper develops a new control design, which reformulates the prediction models by shifting the uncertainties of the first model into the second one, and then uses the reformulated prediction models in the RMPC strategy. This paper will show that compared with the original design, the new control design can enhance the feasibility of the optimisation of control law, reduce the computational burden of the optimisation and also remove the requirement of a sensor for supply air temperature in the original design. Practical applications: The new design method is a further development of a RMPC strategy presented in Xu et al.13 It inherits the benefits of the original control design for practical application, i.e. uncertainties and constraints can be dealt with simultaneously in the design and the robustness of the controlled system can be enhanced. The new design improves the optimisation feasibility, reduces the computational complexity and does not need to measure the supply air temperature. When the new design is adopted to replace the traditional PI control, there is no necessity to change the existent input structure of the PI control. Hence, the new design can be realised in practice easier than the original design.

In this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Levitation control is a core technique of magnetic levitation (Maglev) trains, whose performance has a significant impact on the driving safety and ride comfort during the operation of Maglev trains. With the rapid development of high temperature superconducting (HTS) materials, a novel hybrid levitation system for Maglev trains, composed of HTS and normal conducting electromagnets, is becoming a more promising alternative to the conventional levitation system, due to a lager levitation air gap and lower energy consumption. The controller of the hybrid levitation system is hard to design due to strong nonlinearity, open-loop instability and fast-response requirements. In this study, we propose a robust model predictive control (MPC) strategy for the novel hybrid levitation system in which state constraints are taken into account, including the air gap, and the velocity and acceleration of the hybrid magnet. In the MPC strategy, the prediction model employs a stabilized model through nonlinear and linear state feedback. With regard to the online computational load, the primal-dual interior-point (PDI) algorithm is adopted to solve the optimization problem with high efficiency to deal with constraints in a real-time manner. Finally, simulation results are demonstrated to verify the effectiveness of the proposed MPC-PDI control strategy for the hybrid levitation system, and the significances considering state constraints are revealed. This study provides an engineering realization solution to the novel hybrid levitation system of a Maglev train.

Tube-based robust model predictive control for spacecraft proximity operations in the presence of persistent disturbance

This paper presents a model predictive control formulation that incorporates trajectory sensitivity to improve the robustness of the conventional model predictive control strategy. A numerical example is used to illustrate the potential of this approach. The numerical results suggest that the proposed approach may be an alternative to robust model predictive control strategies when the latter leads to excessive computation requirements or conservatism.

Existing control schemes for 5-DOF robotic manipulators suffer from fundamental limitations: conventional PID controllers cannot handle nonlinear dynamics and coupling effects, adaptive methods exhibit slow response to sudden parameter changes, robust H∞ controllers sacrifice performance for worst-case robustness, and intelligent methods lack formal stability guarantees. These limitations become critical in high-precision applications requiring simultaneous handling of model uncertainties, external disturbances, nonlinearities, and physical constraints. This paper addresses these challenges by proposing a novel integrated control architecture that systematically combines four complementary control methodologies within a unified framework: (1) adaptive H-infinity control providing formal robustness guarantees, (2) Model Predictive Control enabling constraint handling and optimization, (3) Fuzzy Logic control managing complex nonlinearities, and (4) Sliding Mode Control with enhanced disturbance observer for high-frequency noise rejection. The primary contribution is a novel adaptive weighting mechanism that dynamically adjusts each controller's contribution based on real-time performance metrics using exponential functions of tracking error magnitude, ensuring smooth transitions and optimal resource allocation without hard-switching limitations. The integrated framework employs a comprehensive mathematical analysis including composite Lyapunov stability proofs to guarantee asymptotic convergence of tracking error and boundedness of control signals. Rigorous theoretical analysis provides formal convergence guarantees and robustness bounds for parameter variations up to ±30%. The proposed approach is validated through extensive simulations conducted on MATLAB/Simulink using a detailed 5-DOF robotic manipulator model with clearly defined Denavit-Hartenberg parameters, mass distribution, and inertial properties. Simulation results demonstrate significant performance enhancement compared to conventional control methods. The proposed controller achieves superior tracking accuracy with RMS tracking error of 1.35 mm compared to 2.50 mm for H∞ control, 2.87 mm for adaptive control, and 5.58 mm for PD control, representing up to 46% improvement over the best existing robust control method. The system exhibits exceptional robustness with only 11.5% performance degradation under ±30% parameter variations compared to 31.2% degradation for H∞ control and 85.3% for PD control. Disturbance rejection capability is demonstrated with maximum tracking error of 3.21 mm and recovery time of 0.43 s under 5N external force disturbance, significantly outperforming conventional methods.

This paper presents a high-precision control scheme based on active disturbance rejection control (ADRC) to improve the stabilization accuracy of an inertially stabilized platform (ISP) for aerial remote sensing applications. The ADRC controller is designed to suppress the effects of the disturbance on the stabilization accuracy that consists of a tracking differentiator, a nonlinear state error feedback, and an extended state observer. By the ADRC controller, the effects of both the internal uncertain dynamics and the external multisource disturbances on the system output are compensated as a total disturbance in real time. The disturbance rejection ability of the ADRC is analyzed by simulations. To verify the method, the experiments are conducted. The results show that compared with the conventional PID controller, the ADRC has excellent capability in disturbance rejection, by which the effect of main friction disturbance on the control system can be weakened seriously and the stabilization accuracy of the ISP is improved significantly.

A methodology is proposed to design a robust Gain-Scheduled Model Predictive Control (MPC) strategy and to quantify the relative advantages of this controller versus a Linear MPC strategy. For the purpose of analysis and controller design, the process is represented by a nonlinear state-affine model identified from input−output data. This model can be split in linear and nonlinear terms where the linear part is used for controller design and the nonlinear part is accounted for as model uncertainty. Then, robust stability and robust performance tests are formulated based on linear matrix inequalities where the manipulated variables weight of the controllers is tuned to maximize performance. The uncertainty bounds used for the robustness tests are obtained in an iterative fashion by using the frequency response of the manipulated variable with respect to the feedback error. The control strategy performance is quantified by the ratio between the error norm and the disturbance norm. Finally, a case study involving a multiple-input−multiple-output bioreactor is presented. The study is able to predict for which range of operation the Gain-Scheduling MPC surpasses the performance of the Linear MPC.

This paper focuses on the design of a robust tube-based Model Predictive Control law for the control of constrained mobile robots. A time-varying trajectory tracking error model has been used, where uncertainties are assumed to be bounded and additive. The proposed solution to the control problem is a tube-based MPC ensuring robustness and stability. A comparative simulation example is presented showing the promising behavior of the robust MPC controller.

Many robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set

Data-Driven Prediction and Predictive Control Methods for Eco-Driving in Production Vehicles