Robust Tracking Control Research Articles

Model-free optimal robust tracking control for the joint actuated by pneumatic artificial muscles with saturated air pressure input

At present, positioning and tracking the joint angle of the PAM-actuated system is still a challenging issue, due to the inherent hysteresis, high nonlinearities, and time-varying characteristics. Considering the problem of uncertain parameters, external disturbance, and saturated input, a model-free optimal robust tracking control scheme is proposed for the PAMs system in this paper. Also, a nonquadratic cost function is introduced to address the saturation air pressure input. Moreover, an integral reinforcement learning(IRL) algorithm is developed to solve the H∞ tracking Hamilton–Jacobi–Isaacs(HJI) equation. And the IRL algorithm is implemented on a critic–actor-disturbance neural network (NN) structure. The presented control scheme avoids the complete system dynamic and simultaneously compensates for the uncertain parameters, and external disturbance. Then, the effectiveness of the optimal robust tracking controller is verified via computational simulation and keeps the system stable. In addition, the tracking experiment is implemented on a hardware platform, indicating that the presented approach achieves satisfactory tracking performance.

Disturbance suppression based quantized tracking control for periodic piecewise polynomial systems

The investigation presented here deals with the issue of disturbance suppression and the design of robust tracking control with quantization mechanism for periodic piecewise polynomial systems prone to parameter uncertainties, time delays and external disturbances by means of a proportional integral observer (PIO)-based parallel equivalent input disturbance (PEID) approach. Primarily, in the PEID technique, in order to reduce estimate errors, the PEID notion has been put forward, wherein these errors are perceived as artificial disturbances and a chain of EID compensators has been employed to make amends for them. Meanwhile, PIO’s integrating part aids in blending a relaxing variable into the system’s layout, which allows for greater flexibility in the system’s framework while rendering the system more robust. Subsequently, with the information of estimates from PEID and PIO, disturbance suppression-based quantized tracking control is designed, which simultaneously makes the system states follow the reference states and mitigates the disturbances from the system. Further, the input signals are quantized before being sent as a result of the limited capacity of the channel via which the data is transmitted. Subsequently, through configuring a periodic piecewise polynomial matrix and blending Lyapunov stability theory with the matrix polynomial lemma, adequate requirements are derived in the framework of linear matrix inequalities which ensure the desired outcomes. After which, the requisite controller and observer gain matrices are generated by solving the stated linear matrix inequality-based relations. Ultimately, the simulation portion offers a numerical example that verifies the potential of the acquired findings.

A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties

This paper proposes a novel robust tracking control scheme for discrete time linear uncertain Multiple-Input Multiple-Output (MIMO) systems subject to time-varying delay on the states. The considered system is affected by unknown but norm bounded uncertainties on parameters as well as matched disturbances on the states. The designed controller is based upon a proposed novel integral sliding surface and a new switching type of reaching law. Sufficient conditions based on Linear Matrix Inequalities (LMIs) and a suitable Lyapunov–Krasovskii Functional (LKF) are derived in order to guarantee the asymptotic stability of such system. The proposed controller ensures a good tracking performance despite the presence of the time varying delay and the matched/unmatched disturbances. Moreover and thanks to the proposed integral surface, the time reaching phase is eliminated and the chattering phenomenon is significantly reduced. The proposed controller is applied on an Autonomous Underwater Vehicle (AUV) to follow a prescribed desired trajectory. The simulation results illustrate the effectiveness of such controller.

Distributed adaptive event-triggered asymptotic tracking control of linear uncertain multiagent systems by using output only

For the robust tracking control problem of multiagent systems with linear uncertainties, most of the existing studies require full state feedback. Moreover, the designed control strategy also uses global information, such as the number of agents or the eigenvalues of the Laplacian matrix, which does not satisfy the distributed requirement for multiagent design. To address these problems, first, a Luenburger observer is designed to observe the full state of the system by using the output information. Second, the constant gain in the traditional distributed observer for estimating exosystem state information is replaced with a time-varying gain that comes from the output of a newly designed filter, which avoids the use of the global information mentioned above. Finally, based on the above observer and adaptive dynamic feedback, an event-triggered output feedback control strategy is given. This control strategy is not only piecewise constant, which is easy to implement, but also makes the robust tracking control error converge asymptotically to zero. Furthermore, it is theoretically proven that each agent does not have Zeno behaviour, and the effectiveness of the designed control strategy is verified with a simulation example.

Robust adaptive three-dimensional trajectory tracking control for unmanned underwater vehicles with disturbances and uncertain dynamics

Aiming at the three-dimensional (3-D) trajectory tracking problem of UUV with uncertain dynamics in an unknown and bounded external disturbance environment, a new dual closed-loop controller based on nonlinear model predictive control (NMPC) and adaptive integral sliding mode control (AISMC) is designed. The outer-loop NMPC controller designed based on position and attitude tracking errors generates a virtual desired velocity command and transmits it to the inner-loop controller. The inner-loop adaptive integral sliding mode controller based on speed tracking error design combines adaptive radial basis (RBF) neural network controller and disturbance observer to approximate the uncertainty of system model parameters and environmental disturbances, and then generates the actual control input to the UUV system. Different from other cascaded control systems, the designed controller combines the advantages of display processing constraints of MPC and robustness of SMC, which can improve the robustness of the control system, it effectively considers the actual constraints of the system input and state, and avoids the saturation of the actuator. In addition, the stability of the closed-loop system with and without disturbances is proved respectively based on the Lyapunov method. Finally, simulation results verify the effectiveness of the proposed controller: Under the perturbation of 10% model parameters, the UUV can accurately track the desired trajectory.

Robust model reference tracking control for high‐order descriptor linear systems subject to parameter uncertainties

AbstractThis paper investigates the robust model reference tracking control problem for high‐order descriptor linear systems (HODLS) subject to norm‐bounded parameter uncertainties. The problem is divided into two subproblems: a robust proportional plus derivative state feedback stabilization (RPPDSFS) problem and a robust feed‐forward compensation (RFFC) problem. In the presence of uncertainties, by using the controller consisting of RPPDSFS part and RFFC part, all the signals of the closed‐loop system are bounded. The latter is equivalent to seeking three coefficient matrices such that a series of linear matrix equations are satisfied, and simultaneously the effect caused by uncertainties is minimized. Based on the right coprime factorization, the RFFC problem is further converted into a minimization problem with a quadratic performance index and some linear constraints. Thereafter, a linear matrix equation that determines the optimal solution is achieved. The restrictive condition that the coefficient matrix of the augmented reference system is non‐defective is relaxed, which reduces the conservativeness. A numerical example and the application of a three‐axis dynamic flight motion simulator manifest the effectiveness and the practicability of the proposed algorithm.

Differential flatness-based adaptive robust tracking control for wheeled mobile robots with slippage disturbances

Wheeled mobile robots (WMRs) have a wide range of applications in logistics transportation and industrial productions, among which the motion control has always been one of the hot spots in the current WMR researches. However, most of previous designed controllers assumed that the WMR motion had no slippage. Ignoring the slippage factors usually results in a decrease in control performance and even leads to unstable motion. To address such a challenge, a kinematic model with differential flatness is established through dynamic feedback-linearization, which comprehensively considers the multidirectional slippage of mobile robot, including longitudinal and steering slippage. Subsequently, benefited from the one-to-one mapping of states and inputs to flat outputs in differential flat system, an adaptive robust control (ARC) method is proposed to stabilize the system. Different from previous robust control studies, even if the knowledge of the upper bound of system uncertainties is unknown in advance, the proposed adaptive robust controller can still achieve satisfying performance by adaptive estimation of the upper bound of system uncertainties. The effectiveness and feasibility of the proposed method are confirmed by comparative experiments on WMR with slippage disturbance.

Robust consensus tracking control for switched multiple Lagrangian systems by UDE-based control method

The robust consensus tracking control of the switched multiple Lagrangian systems is investigated by the uncertainty and disturbance estimator (UDE)-based control method. Firstly, the switching control method based on the average dwell time (ADT) algorithm is utilized for parameters and network communication topology switching of multiple Lagrangian systems to reduce the impact of load variation and enhance robustness. Then, in two parts, a proposed adaptive UDE-based control method for multiple Lagrangian systems with lumped uncertainty and load variation. In the initial stage, a consensus tracking control of the nominal switched multiple Lagrangian systems is realized via an adaptive backstepping tracker. The UDE control method is integrated and used in the second stage for the exact adjustment of model uncertainties and disturbances as well as asymptotic estimates. It is worth noting that by designing different filters for UDE, it is possible to handle several specified external disturbances that are unbounded. The unified analysis framework of the closed-loop switched control system is realized through Lyapunov analysis. Therefore, the proposed consensus tracking algorithm has a simple structure and good robustness in handling load changes, model uncertainties, and external disturbances. Finally, illustrative examples with computer simulation are provided to verify the effectiveness and correctness of the obtained results.

Robust trajectory tracking control design for the robotic arm with uncertainty and experimental validation

The robotic arm is a complicated system with multiple inputs and outputs, strong coupling, containing uncertainties and nonlinearities. This study proposes a new practical robust control method based on the dynamics model and tracking error, including a model- and error-based proportional-differential feedback term and an error-based robust term. Specifically, the dynamics of the system are modeled using the Lagrangian method. Uncertainties are presumed to be time-varying but limited. Based on the Lyapunov method, the proposed controller has theoretically demonstrated the controlled system with uniform boundedness (UB) and uniform ultimate boundedness (UUB). Furthermore, the radius of the ultimately bounded hypersphere is arbitrarily small based on selecting appropriate design parameters. Based on the two-degree-of-freedom (2-DOF) planar robotic arm experimental platform, the self-developed rapid controller prototype CSPACE-RT is intended to eliminate tedious programming or debugging, significantly simplifying the experimental process. Finally, numerical simulation and experiment results verified the excellent control performance of the suggested controller.

Adaptive robust output tracking of uncertain strict-feedback nonlinear systems with full state constraints via control schemes with simple structure

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results.

Dynamic Modeling and Robust Trajectory Tracking Control of a Hybrid Propulsion-Based Small Underwater Robot

This paper proposes a hybrid propulsion-based small underwater robot for robust trajectory tracking control in a harsh and complex underwater environment. The robot is equipped with a Coanda-effect jet thruster and a pair of propeller-based reconfigurable magnetic-coupling thrusters, allowing it to traverse safely in confined or cluttered spaces as well as cruise efficiently in the open water. To investigate the robot dynamic modeling, we first formulated its simplified mathematical model and estimated the hydrodynamic coefficients by performing the planar motion mechanism using CFD (computational fluid dynamics) simulation. Then, a double-loop trajectory tracking control architecture was designed considering the model uncertainties and environmental disturbances. Based on Lyapunov theory, the outer-loop kinematic control produces the virtual velocity command, while the inner-loop dynamic control adopts the full-state feedback L1-adaptive control to match the command. The asymptotic convergence of the tracking errors and the stability of the whole closed-loop system are guaranteed. Finally, comparative simulations in the presence of unknown disturbances and the variation of model parameters were carried out to verify the robustness of our proposed trajectory tracking control, which is also suitable for the separated son robots.

Using control theory for preventing induced seismicity due to fluid injections in a reservoir

Deep Geothermal Energy, Hydrogen Underground Storage and Carbon Capture Utilization and Storage are promising techniques to satisfy the large-scale needs of the energy sector. However, they all depend on the injection of fluids into the earth’s crust, which, in turn, can cause earthquakes [1, 2]. Earthquakes nucleate when large amounts of elastic energy, stored in the earth's crust, are suddenly released due to abrupt sliding over faults. Fluid injections can create new, or reactivate existing, seismogenic faults and, therefore, cause earthquakes [2, 3].
 More recently, new results for controlling the earthquake instability of a single, natural, mature seismic fault were obtained [4, 5, 6, 7, 8]. These works were based on the mathematical control theory to stabilize and control the underlying physical system, which is underactuated, strongly non-linear and uncertain. The above works could inspire new approaches for preventing induced seismicity too [4, 9].
 In this work, a 3D diffusion equation is considered to model induced seismicity due to fluid injections in a geological reservoir. A robust tracking control is then designed to force the seismicity rate to follow a desired reference, minimize induced seismicity and assure fluid circulation. The designed regulator ensures the control task despite system uncertainties and external perturbations. Simulations of the process are presented to show the reliability and performance of the control approach.

A Robust Adaptive Control Strategy for Electro-hydraulic Servo Based on Friction Compensation

Background: The electro-hydraulic servo system has the advantages of high stiffness, fast response speed, high precision and power-to-weight ratio. Objective: In this patent, an adaptive robust control strategy based on friction compensation is proposed for insufficient control accuracy due to a large number of nonlinearities and uncertainties in the system. Methods: In this patent, the mathematical relationship between the physical quantities of the valve-controlled cylinder is analyzed. Then the mathematical model of valve controlled cylinder considering the main nonlinearity and uncertainty of the system is established. The fuzzy proportion-integral-derivative, deterministic robust, and adaptive robust single-cylinder trajectory tracking controllers are designed and the tracking performance of different reference trajectories is analyzed by MATLAB/Simulink software. Results: In this patent, all the three controllers can track the reference trajectories smoothly. Adaptive robust control strategy can make the uncertain parameters of system converge and approach truth value. Conclusion: In this patent, the adaptive robust control strategy has the function of online parameter adjustment. When tracking accuracy is taken as the index, its tracking effect is better than fuzzy proportion-integral-derivative and deterministic robust.

Nonlinear disturbance observer-based robust predefined time tracking and vibration suppression control for the rigid-flexible coupled robotic mechanisms with large beam-deformations

Nonlinear disturbance observer-based robust predefined time tracking and vibration suppression control for the rigid-flexible coupled robotic mechanisms with large beam-deformations

Distributed Robust Formation Tracking Control for Quadrotor UAVs with Unknown Parameters and Uncertain Disturbances

In this paper, the distributed formation tracking control problem of quadrotor unmanned aerial vehicles is considered. Adaptive backstepping inherently accommodates model uncertainties and external disturbances, making it a robust choice for the dynamic and unpredictable environments in which unmanned aerial vehicles operate. This paper designs a formation flight control scheme for quadrotor unmanned aerial vehicles based on adaptive backstepping technology. The proposed control scheme is divided into two parts. For the position subsystem, a distributed robust formation tracking control scheme is developed to achieve formation flight of quadrotor unmanned aerial vehicles and track the desired flight trajectory. For the attitude subsystem, an adaptive disturbance rejection control scheme is proposed to achieve attitude stabilization during unmanned aerial vehicle flight under uncertain disturbances. Compared to existing results, the novelty of this paper lies in presenting a disturbance rejection flight control scheme for actual quadrotor unmanned aerial vehicle formations, without the need to know the model parameters of each unmanned aerial vehicle. Finally, a quadrotor unmanned aerial vehicle swarm system is used to verify the effectiveness of the proposed control scheme.

Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems

Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems

Robust cooperative tracking of multiagent systems with asymmetric saturation actuator via output feedback

AbstractThe robust tracking control problem of the leader‐follower multiagent systems affected by asymmetric input saturation and external disturbances is addressed in this article, by following three steps. First, an radial basis function neural network (RBFNN) is developed to estimate the external disturbances and supersaturation, where the supersaturation is induced by asymmetric saturation actuator. Second, combining with the developed radial basis function neural network, a reduced‐order observer‐based static protocol and a reduced‐order observer‐based adaptive one are designed for leader‐follower systems with un‐directed communication topology as well as those with directed communication topology, respectively. Third, some mild premises are given to guarantee the semiglobal robust leader‐follower consensus for the above mentioned two kinds of multiagent systems. Finally, the theoretical results are verified by several numerical simulations.

Robust tracking control for uncertain Euler–Lagrange systems via dynamic event‐triggered and self‐triggered ADP

AbstractThis article investigates the robust tracking control problem for a class of Euler–Lagrange systems in presence of parameter uncertainties and external disturbances. Through system transformation and theoretical analysis, an adaptive dynamic programming (ADP) algorithm with two adaptive neural networks (NNs) and a suitable triggering mechanism is proposed to attain the robust stability of the closed‐loop system. A single critic NN is leveraged to implement the approximate optimal controller design. Particularly, an NN‐based feedforward compensation is developed to cope with the uncertainties with unknown bounds. Two different triggering mechanisms are respectively constructed to reduce the budget of sampling, communication and computation, namely the dynamic event‐triggering mechanism (DETM) and the self‐triggering mechanism (STM). The DETM is utilized to decide the update of remote controller and critic NN weight, which can yield a larger inter‐event interval than the static event‐triggering mechanism. Also, the Zeno‐free behavior is guaranteed. Moreover, it is a novel attempt to introduce the STM into ADP design, which relaxes the demand of dedicated hardware online monitoring the event‐triggering condition. Then it is demonstrated that all signals in the closed‐loop system are uniformly ultimately bounded (UUB) via Lyapunov‐based stability analysis. Finally, a simulation example of 2‐link robotic system is implemented to verify the feasibility and effectiveness of the proposed algorithm.

Modified Three-Element Modeling and Robust Tracking Control for a Planar Pneumatic Soft Actuator

In pneumatic soft robotics systems, pneumatic soft actuators (PSAs) are the most important components, so it is necessary to study the precise modeling and control over PSAs for application. This paper focuses on a self-designed planar PSA, named pneumatic bellow actuator (PBA), and proposes a modified three-element model (MTEM) and a nonlinear disturbance observer-based sliding mode control (NDO-based SMC) method to achieve the robust tracking control objective of the PBA with multiple uncertainties. Firstly, the dynamic characteristics of the PBA are analyzed based on experimental data obtained from open-loop experiments of the PBA. Then, based on these dynamic characteristics, a semi-phenomenological MTEM is established considering coupling between the dynamics of the PBA and load as well as friction, which can describe the dynamics of the PBA with changing loads in the rough horizontal plane precisely. Model parameters are then identified by Levenberg-Marquardt (LM) algorithm. Next, identification errors, device disturbances and external disturbances are regarded as the multiple uncertainties of the PBA, and the NDO-based SMC method is proposed based on the MTEM to realize the robust tracking control objective of the PBA. The stability of the control system is proved. The effectiveness of the proposed method is verified by experiments.

Robust trajectory tracking control for cable-driven parallel robots with model uncertainty

This paper is concerned with robust trajectory tracking control for cable-driven parallel robots (CDPRs) with uncertain dynamics. A new accurate trajectory tracking controller (ATTC) is proposed such that the pose of the mobile platform of CDPRs can accurately track a desired trajectory. To further alleviate the input chattering phenomenon, a practical trajectory tracking controller (PTTC) is designed to guarantee the trajectory tracking error is converged to a small neighborhood of the origin. Finally, an illustrative example on a 3-Cable 3-DOF CDPR is provided to evaluate the performance of both ATTC and PTTC, including a comparison study against a typical synchronization controller, which verifies the effectiveness of the proposed controllers.