Estimation-based Control Research Articles

Stability Analysis and Quantitative Tuning of Modified Uncertainty and Disturbance Estimator-Based Control for a Class of Time-Delay Processes

Stability Analysis and Quantitative Tuning of Modified Uncertainty and Disturbance Estimator-Based Control for a Class of Time-Delay Processes

Estimation and Control of Positive Complex Networks Using Linear Programming

This paper focuses on event-triggered state estimation and control of positive complex networks. An event-triggered condition is provided for discrete-time complex networks by which an event-based state estimator and an estimator-based controller are designed through matrix decomposition technology. Thus, the system is converted to an interval uncertain system. The positivity and the L1-gain stability of complex networks are ensured by resorting to a co-positive Lyapunov function. All conditions are solvable in terms of linear programming. Finally, the effectiveness of the proposed state estimator and controller are verified by a numerical example. The main contributions of this paper are as follows: (i) A positive complex network framework is constructed based on an event-triggered strategy, (ii) a new state estimator and an estimator-based controller are proposed, and (iii) a simple analysis and design approach consisting of a co-positive Lyapunov function and linear programming is presented for positive complex networks.

Twin-in-the-loop state estimation for vehicle dynamics control: Theory and experiments

In vehicle dynamics control, many variables of interest cannot be directly measured, as sensors might be costly, fragile or even not available. Therefore, real-time estimation techniques need to be used. The previous approach suffers from two main drawbacks: (i) the approximations due to model mismatch might jeopardize the performance of the final estimation-based control; (ii) each new estimator requires the calibration from scratch of a dedicated model. In this paper, we propose a twin-in-the-loop scheme, where the ad-hoc model is replaced by an accurate full-fledged simulator of the vehicle, typically available to vehicles manufacturers and suitable for the estimation of any on-board variable, coupled with a compensator within a closed-loop observer scheme. Given the black-box nature of the digital twin, a data-driven methodology for observer tuning is developed, based on Bayesian optimization. The effectiveness of the proposed estimation method for the estimation of vehicle states and forces, as compared to traditional model-based Kalman filtering, is experimentally shown on a dataset collected with a sport car. In summary, the proposed approach achieves, in the most aggressive driving scenarios, an average improvement of 0.5° for the side-slip angle estimation, and of more than 500 N for the front lateral forces estimation.

Dynamically Triggered Estimator-Based Controller and Its Application on an Omnidirectional Robot

Dynamically Triggered Estimator-Based Controller and Its Application on an Omnidirectional Robot

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Resilient Consensus for Discrete-Time Multiagent Systems With a Dynamic Leader and Time Delay: Theory and Experiment.

The ever-present cyber-attacks have posed a significant challenge to consensus of multiagent systems (MASs), due to their capability of compromising agents. These threats underscore the critical need to design control strategies that can endow MASs with resilience. In this article, we address resilient consensus problems for first-and second-order discrete-time MASs, considering the presence of malicious agents, a dynamic leader, and communication delay. First, a resilient controller is designed for first-order MASs, and sufficient conditions are derived based on existing robust graph concepts to achieve consensus with ultimately bounded error. Next, since the derived error bound grows factorially with the system scale, a novel graph structure and a modified controller are proposed to limit the growth to a linear rate. Building upon the obtained results, an estimator-based control framework is introduced to solve resilient consensus problems for second-order MASs. Finally, comparative simulations and practical experiments based on unmanned ground vehicles and unmanned-aerial-vehicles are conducted to validate the effectiveness and practicability of the proposed control methods.

Design of Cascade Equivalent-Input-Disturbance Estimator for Control System Under High-Frequency Noise.

This article presents a cascade equivalent-input-disturbance (EID) estimator to handle the control problem of disturbance rejection in the presence of measurement noise. The standard EID estimator faces a challenge when the output of a system suffers from high-frequency noise, i.e., the estimator tuned to achieve high disturbance-rejection performance is usually extremely sensitive to measurement noise. A new estimator is developed in this study to address the issue by combining EID estimators in a unique cascade form. The sensitivity reduction of a cascade EID (CEID) estimator with p levels, which is related to disturbance rejection, is p times larger than that of a standard EID estimator at low frequencies. Meanwhile, the Bode magnitude curve of the transfer function related to noise suppression is shifted up only by 20lgp dB at high frequencies compared to that of a standard one. This improves disturbance-rejection performance and prevents measurement noise from being over-amplified. The design of a CEID estimator-based control system is provided and the stability criterion of the system is derived. The validity and superiority of the presented method are demonstrated by a deep analysis and simulation and experimental results.

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Formation control of multi-agent systems with actuator saturation via neural-based sliding mode estimators

In this paper, the formation control problem for second-order multi-agent systems with model uncertainties and actuator saturation is investigated. An estimator-based robust formation controller is developed to ensure boundedness of the system’s formation tracking error. To estimate uncertain factors without prior knowledge of their Lipschitz constants, two new estimator designs that combine the neural-based estimation process and the sliding mode technique are proposed. Finite-time stability is achieved by introducing a new terminal estimation surface. Regarding the formation controller design, we provide a new framework to study the combined effect of input saturation and input coupling. Both an adaptive compensator and an input regulation algorithm are employed to attenuate state fluctuation led by the reverse effect. Comparative simulations regarding a multi-robot system are conducted to demonstrate the effectiveness of the proposed estimators and the estimator-based controller.

Estimation-based production control of manufacturing–remanufacturing systems with uncertain seasonal return and imprecise demand and inventory

Hybrid manufacturing systems utilising raw materials and returned end-of-life products for production are studied. The systems are failure-prone and subject to inventory, market demand and return uncertainties. Thanks to growing environmental and sustainability concerns, the manufacturing sector is currently experiencing a significant growth in the popularity of reverse logistics. However, the practical implementation of production control in such systems is challenging due to return flow uncertainty and variability. To address this challenge, an estimation-based control using the Kalman filter is proposed in this research. The demand and return models employed contain random and deterministic components, with the latter being time-invariant for demand and uncertain with seasonal variations for return. The processing steps used include the estimation of inventory levels and demand and return components, return forecasting allowing cost computation over a long horizon, and the determination of the production and disposal policies adapting to market variations and uncertainties. We classify the systems according to relationships between their production capacity, demand and return ranges. We then present an extensive numerical study of optimal policies for various system classes and show that adaptive policies outperform the conventional ones, thus proving the effectiveness of the proposed production control approach for complex industrially oriented systems.

Nonlinear optimal control of a multi-rotor wind power unit with PMSGs and AC/DC converters)

A nonlinear optimal (H-infinity) control method is developed for a wind power unit that comprises twin turbines, permanent magnet synchronous generators (PMSGs) and AC/DC converters. By proving differential flatness properties for this system the associated setpoints definition problem is solved. The dynamic model of the wind power unit being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearisation around a temporary operating point that is recomputed at each time-step of the control method. The linearisation relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearised state-space model of the wind power unit, a stabilising optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the wind power unit under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the wind power unit, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator.

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Performance optimization of electromagnetic levitation system based on gradient estimator

Aiming at the problem of optimal design of the controller of electromagnetic levitation system, this paper proposes a gradient estimator-based controller design and optimization structure suitable for electromagnetic levitation system. The structure consists of a nominal controller, a residual generator, and a dynamic compensator. The controller structure can further improve the anti-disturbance and robustness of the electromagnetic levitation system on the premise of ensuring the stability and reliability. Considering the generality of electromagnetic levitation system, the proportional–integral–derivative (PID) controller is selected as the nominal controller, and the robustness of the system is improved by the dynamic compensator based on the residual generator. The parameter design and update strategy of dynamic compensator based on gradient estimator are proposed, and the expression of gradient estimator is designed and deduced. Taking the single-degree-freedom electromagnetic levitation experimental platform as an example, the simulation and experimental results show that the structure has strong robustness to shock disturbances. Compared with the PID controller, the range of the gap fluctuation is smaller after the instantaneous impact interference, and the anti-interference capability of the electromagnetic levitation system is improved.

Nonlinear optimal control for a gas compressor driven by an induction motor

The article proposes a nonlinear optimal control approach for the dynamic model of a gas centrifugal compressor being driven by an induction motor (IM). The dynamic model of the integrated compressor-induction motor system, being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the compressor-IM a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the compressor-IM under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the compressor-IM, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator. The differential flatness properties of the compressor-IM system are proven. The article’s method provides one of the few algorithmically simple and computationally efficient solutions for the nonlinear optimal control problem of the compressor-IM system.

Formation Tracking of Multiagent Systems With Time-Varying Actuator Faults and Its Application to Task-Space Cooperative Tracking of Manipulators.

This article is concerned with a fault-tolerant formation tracking problem of nonlinear systems under unknown faults, where the leader's states are only accessible to a small set of followers via a directed graph. Under these faults, not only the amplitudes but also the signs of control coefficients become time-varying and unknown. The current setting will enhance the investigated problem's practical relevance and at the same time, it poses nontrivial design challenges of distributed control algorithms and convergence analysis. To solve this problem, a novel distributed control algorithm is developed by incorporating an estimation-based control framework together with a Nussbaum gain approach to guarantee an asymptotic cooperative formation tracking of nonlinear networked systems under unknown and dynamic actuator faults. Moreover, the proposed control framework is extended to ensure an asymptotic task-space coordination of multiple manipulators under unknown actuator faults, kinematics, and dynamics. Lastly, numerical simulation results are provided to validate the effectiveness of the proposed distributed designs.

State-constrained bipartite tracking of interconnected robotic systems via hierarchical prescribed-performance control

This paper investigates the collaborative design problem aiming to achieve state-constrained bipartite tracking of the interconnected robotic systems (IRSs) with prescribed performance. In practical applications, the physical limitations of the robots are inevitable. Besides, it is difficult to ensure that the target trajectory is known for each robot of the IRSs in advance. Thus, it is important to follow the target trajectory and meanwhile obey the state constraint being generated from the physical limitations and the external environment of the IRSs. To this end, we propose a new hierarchical state-constrained estimator-based control framework with the characteristics of low computation complexity and high task adaptability. With limited accessibility of the target trajectory, we newly present the estimator to observe it at each time interval through the interconnections among the robots. The state constraint is never violated throughout the convergence process by using the presented control algorithm. The theoretical proof and simulation results are presented to validate the feasibility of the control framework.

Robust tuning of uncertainty and disturbance estimator-based control for stable processes with time delay

To expand the potential of uncertainty and disturbance estimator (UDE)-based control in practical application to most industrial stable processes, this paper proposes a convenient yet robust tuning rule according to the widely used first-order plus time delay (FOPTD) plant. The Smith predictor is first introduced to anticipate the delay-free output, which guarantees signal synchronizations in three control modules and enables remarkable restorations of nominal stability and performance. Then a second-order filter is employed in UDE to decouple the trade-off between disturbance rejection and noise attenuation. Based on this improvement and fixing both tracking speed and feedback gain to suggested patterns, the exhaustive evaluations for robustness against model distortion are executed through scanning the dimensionless filter bandwidth. The boundary demarcation triggered by the plunge of the continuous range of tolerable mismatched delays subsequently facilitates the formulation of an intuitive tuning rule with prescribed robustness. Its inherent model-based scaling property largely enables this rule to be implemented readily in industrial processes just like the proportional-integral-derivative (PID) controller. Several representative simulations are performed to demonstrate the merits of the proposed method over the related control strategies. And the promising prospect of the UDE-based control in the practical application is further illustrated by conducting a water level control experiment.

Bearing-Based Formation Maneuver Control of Leader-Follower Multi-Agent Systems

In this paper, we study the bearing-based formation maneuver control problem of the leader-follower multi-agent system. The objectives are achieving the rotation, translation, and scaling maneuvers with a transformable formation shape. Unlike existing works where the target formation is defined by displacements, distances, or constant bearings, we propose a novel target formation with time-varying bearings. The feasibility and uniqueness of the target formation are analyzed by extending the properties of bearing rigidity to time-varying cases. Compared to the existing methods where the positions and velocities of all the agents are required, an estimation-based control method is proposed to achieve the target formation using relative bearings and only the leaders’ positions and velocities. Both the estimation error and tracking error converge to zero under the extended properties of bearing rigidity and cascade system theories. A sufficient condition for collision avoidance among the agents is also proposed. A numerical example illustrates the effectiveness of the proposed method.

Bearing-Based Target Entrapping Control of Multiple Uncertain Agents With Arbitrary Maneuvers

This paper is concerned with bearing-based cooperative target entrapping control of multiple uncertain agents with arbitrary maneuvers including shape deformation, rotations, scalings, etc. A leader-follower structure is used, where the leaders move with the predesigned trajectories, and the followers are steered by an estimation-based control method, integrating a distance estimator using bearing measurements and a stress matrix-based formation controller. The signum functions are used to compensate for the uncertainties so that the agents’ accelerations can be piecewise continuous and bounded to track the desired dynamics. With proper design of the leaders’ trajectories and a geometric configuration, an affine matrix is determined so that the inter-agent relative bearings can be persistently exciting since the bearing rates are related to different weighted combinations of the affine matrix vectors. The asymptotic convergence of the estimation and control error is proved using Filipov properties and cascaded system theories. A sufficient condition for inter-agent collision avoidance is also proposed. Finally, simulation results are given to validate the effectiveness of the method.

Nonlinear Optimal Control for the Nine-Phase Permanent Magnet Synchronous Motor

Abstract Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They exhibit advantages comparing to three-phase motors because of achieving high power and torque rates under moderate variations of voltage and currents in their phases, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine-phase PMSM undergoes an approximate linearization process at each sampling instance. The linearisation procedure is based on first-order Taylor-series expansion and on the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion is satisfied, which signifies robustness of the control scheme against model uncertainty and perturbations. Moreover, under mild assumptions it is also proven that the control loop is globally asymptotically stable. Additionally it is experimentally confirmed through simulation tests, that the nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to apply state estimation-based control without the need to measure the entire state vector of the nine-phase PMSM, the H-infinity Kalman Filter is used as a robust state estimator.