Robust Nonlinear Model Predictive Control Research Articles

Real-time and hardware in the loop validation of electric vehicle performance: Robust nonlinear predictive speed and currents control based on space vector modulation for PMSM

The transport industry's environmental impact has prompted various stakeholders to focus more on electric vehicles as a potential solution. Extensive research on electric vehicle motor control reveals their complexity, highlighting the crucial role of the traction motor control mechanism being one of their essential subsystems. This study presents a novel approach to control the drive system of an electric vehicle's permanent magnet synchronous motor, using a robust non-linear model predictive control in a cascaded structure combined with a space vector modulation technique. The formulation of the robust non-linear model predictive control law involves optimizing a new cost function with the inclusion of an integral action in the controller to ensure zero steady-state error. An important aspect of this control approach is its ability to enhance robustness without needing information about external perturbations and parameter uncertainties. Moreover, the space vector modulation technique is designed to address the issue of current harmonic distortion by carefully selecting appropriate switching vectors. The appropriate selection for space voltage vectors for every sampling period maintains a consistent switching frequency. As a result, the SVM can enhance torque-rippled regulation and accomplish effective flux and torque control. The performance of the proposed control system is evaluated through a series of numerical simulations using MATLAB/Simulink. The simulation results are analyzed and compared to assess the effectiveness of the proposed control system in terms of tracking accuracy, disturbance rejection, robustness against parameter uncertainties, reduction of torque, and current ripples. To further validate the numerical simulation results, a hardware-in-the-loop (HIL) setup is established using the OPAL-RT platform. Furthermore, experimental validation on a PMSM utilizing the dSPACE DS1202 board is carried out, demonstrating the efficacy of the proposed control system. These findings validate the suggested control technique's robustness and efficiency.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

Robust tube-based NMPC for dynamic systems with discrete degrees of freedom

We present a robust nonlinear model predictive control (NMPC) algorithm for dynamic systems with mixed degrees of freedom, i.e., continuous and discrete manipulated variables. The discrete variables are often excluded from the NMPC layer and determined at a supervisory layer, which typically leads to suboptimal solutions. In contrast, the proposed controller optimizes both classes of degrees of freedom within the NMPC layer, thereby enhancing the closed-loop performance. Our approach relies on a computationally efficient relaxation and integrality restoration strategy. Initially, a nominal controller computes relaxed central reference trajectories for the states and the input variables. These trajectories are then tracked by an ancillary NMPC controller before the integrality of the discrete variables is restored. The role of the ancillary controller is to ensure robustness against the integer restoration error as well as other disturbances based on a nonlinear Tube MPC approach. Furthermore, we provide sufficient conditions to establish recursive feasibility and guarantee robust closed-loop stability. Finally, the effectiveness of the approach is demonstrated through two nonlinear simulation examples, affirming its viability and robustness.

Knee extension tracking and fatigue regulation results using a robust MPC approach in a hybrid exoskeleton

A nonlinear model predictive controller (NMPC) is a promising approach for cooperative control of functional electrical stimulation (FES) and an exoskeleton to assist limb function in people with spinal cord injury (SCI). Potentially, the cooperative control can mitigate the effects of FES-induced muscle fatigue, a significant technical challenge impeding the clinical translation of FES. However, previous NMPC-based cooperative designs have been limited to limb regulation and may not include fatigue regulation in the control objective. In this paper, we design a new NMPC law for limb tracking and fatigue regulation and present experimental results from participants with no disability and a participant with SCI. For robust tracking, this paper augments the NMPC with a Lyapunov-based feedback controller. A terminal controller and terminal constraint regions are specifically derived to show the robust NMPC scheme’s recursive feasibility and to satisfy the input constraints. The experimental results of continuous knee tracking show dynamic allocation of exoskeleton assistance despite decreasing control effectiveness of FES due to muscle fatigue. The robust tube-based MPC reduced the knee angle’s root mean square tracking error by 34% compared to a nominal MPC. It elicited cooperative behavior when it automatically modulated (increased or decreased) FES and motor inputs for different desired fatigue levels while maintaining desired knee angle tracking performance. The statistical t-test showed that the FES input was significantly reduced in the post-fatigue trial (with the desired fatigue level of 1), and the muscle was significantly less fatigued compared to the pre-fatigue experiment (with the desired fatigue level of 0.5).

Robust Nonlinear Model Predictive Control of an Autonomous Launch and Recovery System

Robust Nonlinear Model Predictive Control of an Autonomous Launch and Recovery System

Multi-scenario and multi-stage robust NMPC with state estimation application on the Tennessee-Eastman process

This study presents the implementation of two discrete robust approaches to Non-linear Model Predictive Control (NMPC), multi-scenario NMPC (MSc-NMPC) and multi-stage NMPC (MS-NMPC), to the benchmark Tennessee-Eastman (TE) challenge, with Extended Kalman Filter (EKF) and Moving Horizon Estimation (MHE) as state estimators. The robust NMPC formulation results in closed-loop responses that prevent constraint violation and closely track the process set-point under parameter uncertainty, even in scenarios where traditional NMPC results in an unstable response for this process. Additionally, unconstrained state estimators such as EKF are unsuitable because the parameter uncertainty may cause estimates to fall outside the feasible region of the process, which ultimately destabilizes the process. MHE was able to overcome this challenge because it considers process constraints in its formulation. The additional computational time required to solve the robust NMPC formulations and MHE does not cause significant delays for the sampling time considered, demonstrating their applicability to challenging large-scale industrial chemical processes.

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

AbstractThis paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete‐time nonlinear systems capable to deal with changing setpoints and unknown non‐additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non‐additive non‐slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed‐loop input‐to‐state stability and recursive feasibility of the optimization problem for any piece‐wise constant setpoint and non‐additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

Generalized robust MPC with zone-tracking

We propose a robust nonlinear model predictive control design with generalized zone tracking (ZMPC) in this work. The proposed ZMPC has guaranteed convergence into the target zone in the presence of bounded disturbance. The proposed approach achieves this by modifying the actual target zone such that the effect of disturbances is rejected. A control invariant set (CIS) inside the modified target zone is used as the terminal set, which ensures the closed-loop stability of the proposed controller. Closed-loop stability analysis is presented. Simulation studies based on a continuous stirred tank reactor (CSTR) are performed to validate the effectiveness of the proposed ZMPC.

Robust control designs for microalgae cultivation in continuous photobioreactors

Abstract Microalgae are used to produce renewable biofuels and high-value components and in bioremediation and CO2 sequestration tasks. These increasing applications, in conjunction with a desirable constant large-scale productivity, motivate the development and application of practical controllers. This paper addresses the application of robust control schemes for microalgae cultivation in continuous photobioreactors. Due to the model uncertainties and external perturbations, robust control designs are required to guarantee the desired microalgae productivity. Furthermore, simple controller designs are desirable for practical implementation purposes. Therefore, two robust control designs are applied and evaluated in this paper for two relevant case studies of microalgae cultivation in photobioreactors. The first control design is based on an enhanced simple-input output model with uncertain estimation. The second control design is the robust nonlinear model predictive control considering different uncertain scenarios. Numerical simulations of two case studies aimed at lipid production and CO2 capture under different conditions are presented to evaluate the robust closed-loop performance.

Distributed time‐varying optimization control for multirobot systems with collision avoidance by hierarchical approach

AbstractIn this article, a distributed time‐varying optimization problem for multirobot systems with collision avoidance is studied. A hierarchical control framework is employed to simplify the complex problem into two subproblems in two layers. One is the network layer where a novel distributed time‐varying finite‐time optimal control protocol as a signal generator is proposed for each robot. The signal generator ignores the model constraint and uncertainty. The other is the real‐time layer, which mainly contains a sampling module and a robust nonlinear model predictive control (NMPC) module. The former samples the optimal signal from the signal generator as a series of sampling tracking points with proper distance to improve tracking performance, and the latter searches for the optimal control protocol for the robot system to track these sampling tracking points in sequence with the model constraint and uncertainty. Furthermore, considering the collision between each robot, a give‐way strategy is designed that the robot with a low priority has to stop to wait for the other with a high priority to move first. And a primary‐secondary judgment technology determines the priorities of robots adaptively according to the current state of the robots. If the way forward of the moving robot is blocked by the stopping one, an auxiliary point is introduced as a temporary transfer station to avoid collision further. Finally, the effectiveness of the proposed methods is verified by a simulation example.

Disturbance Observer-Based Prescribed Performance Predictive Control for Spacecraft On-Orbit Inspection

Spacecraft on-orbit inspection provides a prerequisite for the subsequent autonomous proximity operations. To fulfill the mission, robust constrained control algorithms for relative position tracking and attitude adjustment should be employed to handle the nonlinear coupled dynamics, system constraints, and external disturbances. In this paper, a robust nonlinear model predictive control (NMPC) scheme with prescribed performance based on a fixed-time neural network disturbance observer is proposed. Predefined tracking performance requirements are achieved, and, meanwhile, safety and stability are guaranteed. By exploiting the prescribed performance control technique, the proposed NMPC structure is capable of establishing a quantitative relationship between design parameters and certain prespecified performance values. Moreover, the proposed fixed-time neural network disturbance observer shows superiority in the disturbance estimations due to the property of universal approximation and fixed-time convergence. To illustrate the capabilities of our algorithm, comparison simulation tests concerning with prescribed performance and disturbance estimating are presented. Selection of tuning parameters is discussed, and computational load of the proposed algorithm is profiled.

Robust nonlinear model predictive control of a bionic underwater robot with external disturbances

Aimed at the trajectory tracking control problem of bionic underwater robots, this paper designs a novel two-dimensional trajectory tracking method based on robust nonlinear model predictive control (RNMPC) and a central pattern generator (CPG) for use in the trajectory tracking of a bionic underwater robot with an external disturbance. First, the overall mathematical model of the robot is established, a robust nonlinear model predictive controller based on a tube for trajectory tracking is designed, and then the stability of the controller is proved by the Lyapunov stability analysis method. Second, a transformation function is designed to combine the CPG motion controller at the bottom layer and the RNMPC trajectory tracking controller at the upper layer in order to establish an RNMPC-CPG controller, which improves the coordination and smoothness of the motion of the bionic robot in the trajectory tracking process. Finally, a simulation experiment is designed to verify the tracking performance of the bionic underwater robot with external disturbances. The simulation results demonstrate the effectiveness of the controller.

Approximate two‐loop robust nonlinear model predictive control with real‐time execution and closed‐loop guarantee

AbstractIn this article, a robust nonlinear model predictive control (NMPC) scheme with two control loops is considered and its real‐time execution is guaranteed for a predefined sampling time. Robustness of the NMPC scheme against bounded input uncertainty is achieved by assuming Lipschitz continuity of the inner‐loop dynamic function. The NMPC control law is approximated using piecewise affine linear functions over hyper‐rectangle regions generated by k‐d tree partitioning algorithm. Additionally, error bound on the approximation of the optimal solution function is obtained by assuming bounds on the subgradient of the optimal solution function. Consequently, the robust stability and recursive feasibility of the closed‐loop system for the proposed approximate NMPC framework are proven, and at the same time, real‐time execution of the proposed scheme for a predefined sampling time is guaranteed. Simulation results, on a nonlinear benchmark problem, are used to better illustrate the proposed approach and to compare it with some other methods.

Adaptively robust nonlinear model predictive control based on attack identification

Abstract Robust model predictive control (MPC) is an essential tool for control systems under uncertainty as it allows for constraint satisfaction even if disturbances occur. When a system suffers malicious attacks, in contrast to parametric uncertainties or known systems faults, it is difficult to specify tight uncertainty ranges within which possible disturbances lie. In this case, very conservative solutions or even infeasible problems are obtained. To address this issue, we propose an adaptively robust MPC scheme that adjusts the uncertainty ranges to available knowledge about the attackers. To this end, we combine a recently proposed method identifying unknown attacks on nonlinear systems with a multi-stage approach to robust MPC. We illustrate the potential of the method in a numerical case study with a distributed nonlinear system.

Robust nonlinear model predictive control of cascade of fermenters with recycle for efficient bioethanol production

In this paper, dynamical behavior and control of the continuous ethanol fermentation process are studied. The process productivity is improved by using two fermenters connected in series with recycle of cells. First, dynamical behavior and productivity of the cascade system are studied by using numerical bifurcation analysis. Then, multi-stage nonlinear model predictive control (MS-NMPC), classical and offset-free NMPCs algorithms are designed to eliminate the undesired oscillations. To ensure acceptable efficiency of the cascade process, a minimal ethanol concentration is defined and included as additional constraint in the controller design. The unmeasured state variables are estimated by using the asymptotic observer. It is shown that for smaller sampling times the predictive controllers are very effective, even in presence of parameter uncertainties. It is also observed that offset-free NMPC algorithm is more sensitive to measurement noise, but MS-NMPC and classical NMPC are more sensitive to estimation errors for longer sampling times.

Robust nonlinear model predictive control based on nominal predictions with piecewise constant references and bounded disturbances

AbstractThis article presents a robust nonlinear model predictive control (NMPC) strategy for constrained systems with piecewise constant references and bounded disturbances based on nominal predictions. An artificial target is employed to avoid feasibility loss due to target change and to provide a potentially enlarged domain of attraction. Recursive feasibility and input‐to‐state stability are ensured. Recursive feasibility is guaranteed due to the tighter constraints that are recursively computed offline based on the disturbance reachable sets. The zonotopic approach from the mean‐value theorem extension is applied to compute these tighter constraints. In the presence of stochastic disturbances with known distribution, individual chance constraints can be considered in the proposed NMPC algorithm. Furthermore, simplified stabilizing ingredients are proposed in order that the robust assumptions hold based on standard algorithms. Case studies based on the continuous stirred tank reactor and buck‐boost control benchmarks are presented to illustrate the main properties of the proposed approach.

Robust Tube-Enhanced Multi-Stage NMPC With Stability Guarantees

We propose a robust Nonlinear Model Predictive Control (NMPC) scheme that provides an improved trade-off between optimality and complexity when compared to other available strategies. Two controllers are employed in the proposed framework: A multi-stage primary controller that optimizes a given objective in the presence of uncertainties with tightened constraints and a multi-stage ancillary controller that tracks the predicted tree of state and input trajectories of the primary controller. The primary controller optimizes the original objective by considering different realizations of the most significant uncertainties in the predictions. The ancillary controller provides robustness against other uncertainties by tracking the predicted tree of state and input trajectories of the primary controller. We establish sufficient conditions for closed-loop stability. The advantages of the scheme are demonstrated for a continuous stirred tank reactor (CSTR) example.

Robust Nonlinear Model Predictive Control for Ship Dynamic Positioning Using Laguerre Function

This paper is devoted to the issue of computationally efficient and robust nonlinear model predictive control (NMPC) for ship dynamic positioning (DP) systems subjected to input constraints and unknown environmental disturbances. The Laguerre functions, typically applied to the linear systems, are introduced to the constrained NMPC design of the nonlinear DP system to reduce the computational burden. The unscented Kalman filter is adopted to estimate the unknown disturbances and states; thus, the disturbance estimates are utilized as the cancellation signal to achieve robust offset-free control. Simulations of the proposed Laguerre function-based NMPC scheme are implemented and compared with the performance of typical Laguerre function-based linear model predictive control (LMPC) for the DP system. Simulation results well demonstrate the effectiveness, robustness and superiority of the proposed controller.

Robust Nonlinear Model Predictive Control With Model Predictive Sliding Mode for Continuous-Time Systems

Abstract This paper presents a robust, tube-based nonlinear model predictive controller for continuous-time systems with additive disturbances which cascades two sampled-data model predictive controllers: the first creates a desired path using nominal dynamics, and the second maintains the true state close to the nominal state by regulating a sliding variable designed on the error between the true and nominal states. The sampled-data model predictive approach permits easy incorporation of continuous-time sliding mode dynamics, allowing a dynamic boundary layer and tube design to be included. In this way, the control applied to the system capitalizes on the robustness properties of traditional sliding mode control (SMC) while incorporating system constraints. Stability analysis is presented in the context of input-to-state stability (ISS) for continuous-time systems. The proposed controller is implemented on two case studies, is compared to benchmark tube-based model predictive controllers, and is evaluated using average root-mean-square (RMS) values on the state and input variables, in addition to average integral square error (ISE) and integral absolute error (IAE) values on the position states. Results reveal that the proposed technique responds to higher levels of disturbance with significant increases in control effort, eliminates constraint violation by using of constrained SMC as the secondary controller, and maintains similar tracking performance to benchmark controllers at lower levels of control effort.

Robust Nonlinear Model Predictive Control with Bounded Disturbances Based on Zonotopic Constraint Tightening

Robust Nonlinear Model Predictive Control with Bounded Disturbances Based on Zonotopic Constraint Tightening