Tracking Error Dynamics Research Articles

MPPT Novel Controller Based on Passivity for the PV Solar Panel-Boost Power Converter Combination

This article deals with the MPPT controller based on passivity, which calculates through a dynamic average model between the PV solar panel and the boost power converter under uniform irradiance conditions. The MPPT algorithm is a linear controller based on the exact tracking error dynamics passive output feedback (ETEDPOF) controller design methodology. The algorithm includes suitable adaptive feedforward pre-compensation, which explicitly depends on the precisely estimated resistance of the boost converter. The MPP reaches by regulating the voltage and current of the boost converter to hold the PV maximum power in the system's input capacitor. The controller desired references such as the inductor current, the output voltage, and the average input control are in terms of the PV maximum power nominal values, which remain always fixed. A reduced-order extended state observer (RESO) develops to estimate the boost converter's output resistance, adapting to the controller's desired references. Simulation and experimental results demonstrate the effectiveness, stability, and robustness of the MPPT algorithm based on passivity as compared to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Incremental Conductance</i> (IC) algorithm, under sudden output resistor changes, high irradiance, and high temperature in the solar panels.

A set-based approach for detecting faults of a remotely controlled robotic vehicle during a trajectory tracking maneuver

This paper addresses the problem of fault detection for a remotely controlled Differential Drive Mobile Robot (DDMR) during trajectory tracking maneuvers. The proposed solution involves two steps. The first step, performed offline, consists of generating a feasible trajectory for the DDMR subject to unknown but bounded external disturbances. To this end, the dynamics of the closed-loop trajectory tracking error are first described using an uncertain system with norm-bounded uncertainty. The optimal feasible trajectory is obtained by a recursive algorithm that involves solving some SDP optimization problems with LMIs constraints. In the second step, which is performed online, the feasibility property of the computed trajectory is exploited to detect faults during the tracking maneuvers. In order to validate the proposed approach, an extensive experimental test campaign was conducted using the Jaguar V4 Dr.Robot platform.

Performance analysis of distributed power systems using error dynamics passive output feedback control

This paper presents a novel control approach for integrated converters using Exact Tracking Error Dynamics Passive Output Feedback control and Exact Static Error Dynamics Passive Output Feedback control. By continuously injecting active distributed power systems (DPS) power sources into the utility grid and loads, the approach reduces harmonic current distortion and maintains unity for the grid’s power factor. The paper compares existing control methods, such as P, PI, proportional–integral–derivative (PID), energy structuring and damping infusion and interconnection and damping assignment—passivity-based control and considers the impacts of instantaneous fluctuations in reference current elements on the AC side and oscillations in DC voltage generated by the DC-link voltage. Relevant switching state functions are designed, and if the maximum power can be fed exceeds the required power from grid-connected loads, the true, reactive, and harmonic current elements of loads are adjusted dynamically, resulting in in-phase sinewave grid currents. The performance analysis is performed using MATLAB/Simulink, and a smaller research prototype is built and discussed.

A robust adaptive formation control methodology for networked multi-UAV systems with applications to cooperative payload transportation

This paper develops a new robust adaptive formation control methodology for networked multi-UAV systems to solve the cooperative payload transportation problem. This methodology offers a simple yet effective technique for object transportation relying on the formation tracking principle in the presence of bounded exogenous disturbances. Compared to existing techniques, the proposed method resorts to the σ-modification approach to resolve the parameter drift phenomenon. The ultimate boundedness of the formation tracking error dynamics is established by utilising Lyapunov theory. In addition, the proposed scheme does not involve any multi-body dynamics problem, nor does it require any reference model, disturbance filter/estimator or any prior knowledge of the disturbances. As a result, it reduces the overall complexity of the formation control scheme. The paper includes extensive simulation case studies accompanied by lab-based experimental validation results conducted on a group of nano quadcopter UAVs to demonstrate the feasibility and performance of the controller. The paper also projects a potential application of the proposed scheme in cooperative payload transportation missions.

Multiagent-Based Consensus Optimal Control for Microgrid With External Disturbances via Zero-Sum Game Strategy

Due to the fact that the external disturbances are unavoidable in nonlinear microgrids (MGs) systems, which could induce the oscillate of controller, leading to the excessive line loss, and the nonlinear could also result in the controller design difficulty in MGs. Therefore, based on the distributed consensus algorithm of multi-agent systems, this paper studies the distributed voltage recovery consensus optimal control problem for the MGs with nonlinear item and external disturbances. Firstly, the distributed secondary voltage restoration consensus control problem can be transformed into a distributed zero-sum (ZS) differential game problem of the voltage restoration consensus tracking error dynamics via applying the adaptive command-filtered backstepping technique, in which the auxiliary system and neural networks (NNs) are introduced to solve the unknown nonlinearities and external disturbances. Subsequently, the distributed voltage restoration consensus optimal control protocol is constructed via ZS differential game algorithm to achieve the voltage recovery of island MGs, in which a critic network is proposed to estimate the associated cooperative cost function online with a designed weight update law. Further, the consensus optimal control protocol proposed not only ensures the cooperative cost function to be minimized, but also ensures in the closed-loop systems all signals to be cooperatively uniformly ultimately bounded (CUUB). In addition, based on the Lyapunov stability theory, it is proved that the voltage recovery synchronization error can converge to an arbitrarily small range near the origin. Finally, simulation results verify the effectiveness of the proposed controller in island MG.

A composite adaptive robust control for pneumatic servo systems with time-varying inertia

This article proposes a composite adaptive robust control for a pneumatic servo system with time-varying inertia to achieve a good tracking performance. The proposed design not only preserves the merits of both direct adaptive robust control and indirect adaptive robust control but also obtains a better performance of the working condition with time-varying inertias. Firstly, prescribed tracking performance is guaranteed without knowing the bounds of parametric and non-parametric uncertainties by leveraging a discontinuous projection and deterministic robust control technique. And a nonlinear tracking differentiator is used to obviate differential signal in backstepping. Secondly, the online parametric estimation algorithm is developed by intelligently integrating tracking error dynamics and physical plant dynamics. By effectively using the information of both tracking error and prediction error, a high adaptation gain can be used for achieving a faster parameter convergence and smaller tracking error. Moreover, exponential convergence of both tracking error and prediction error can be obtained under certain conditions. Lastly, comparative experiments on different conditions are carried out for a single-rod pneumatic cylinder driven by a proportional directional valve to demonstrate the superiority of the proposed method.

Neural Network Based Control of Four-Bar Mechanism with Variable Input Velocity

For control applications, the angular velocity of the drive crank of a four-bar mechanism is traditionally assumed to be constant. In this paper, we propose control of variable velocity of the drive crank to obtain the desired output motions for the coupler point. To estimate the reference trajectory for the crank velocity, a neural network is trained with data from the kinematic model. The control law is designed from feedback linearization of the tracking error dynamics and a Proportional–Integral–Derivative (PID) controller. The applicability of the proposed scheme is validated through simulations for three variable speed profiles, obtaining excellent results from the system.

Online adaptive optimal tracking control for model-free nonlinear systems via a dynamic neural network

This paper presents an online adaptive approximate solution for the optimal tracking control problem of model-free nonlinear systems. Firstly, a dynamic neural network identifier with properly designed weights updating laws is developed to identify the unknown dynamics. Then an adaptive optimal tracking control policy consisting of two terms is proposed, i.e. a steady-state control term is established to ensure the desired tracking performance at the steady state, and an optimal control term is proposed to ensure the optimal tracking error dynamics optimally. The composite Lyapunov method is used to analyse the stability of the closed-loop system. Two simulation examples are presented to demonstrate the effectiveness of the proposed method.

Robust preview control of interconnected continuous-time systems with parametric uncertainties

This paper designs a decentralized robust preview tracking controller for interconnected continuous-time systems with parametric uncertainties. The uncertain error system, which is composed of the derivative equation of the states, the tracking error dynamics, and the available future reference dynamics, is constructed. Then, a cost function is introduced to evaluate the tracking quality. Meanwhile, a performance signal is defined to discuss the influence of disturbances on the tracking performance. Based on the above operations, the considered tracking control is converted to the H-infinity control of the uncertain error system. The sufficient conditions which guarantee that the closed-loop system is asymptotically stable with H-infinity disturbance attenuation are derived. Further, the decentralized preview controller is obtained with the help of the linear matrix inequality (LMI). The result is applied to double-parallel inverted pendulum system and 3-interconnected machine power system. Numerical simulation demonstrate that the suggested preview controller can make the output track the reference signal, and the tracking quality be improved as the preview length increases.

Trajectory Tracking in Unicycle Mobile Robots: A Homogeneity–based Control Approach

This paper contributes to the design of a family of homogeneous controllers to deal with the trajectory tracking problem in unicycle mobile robots (UMRs). The control strategy is based on a cascade control paradigm, which includes the position and orientation tracking error subsystems. The proposed homogeneous controllers provide different types of convergence to zero for the tracking error dynamics, i.e., asymptotic, exponential, and finite-time convergence. Simulation results illustrate the performance of the proposed family of homogeneous controllers.

Attention-Enabled Memory for Concurrent Learning Adaptive Control

Transient tracking error dynamics are inevitable in any practical closed-loop control system. While numerous works are devoted to improving these dynamics, in this letter, we focus on taking advantage of it first, in the context of adaptive control. We propose a memory architecture that can make use of stored significant data about the transients of previously experienced anomalies to aid in obtaining a resilient system against uncertainties. The proposed architecture consists of 1) a memory containing data about a variety of uncertainties, 2) a short-term memory that aids in handling new uncertainties, and 3) an attention-based reading mechanism that enables the controller to retrieve only relevant data from the memory. The effectiveness of the architecture is validated through numerical simulations, and a rigorous Lyapunov stability analysis is provided.

Super-twisting sliding-mode observer-based model reference adaptive speed control for PMSM drives

This paper develops a super-twisting sliding-mode observer-based model reference adaptive speed controller (STSMO-MRA-SC) for the permanent-magnet synchronous motor-based variable speed drive (PMSM-VSD) system. A stable first-order linear model is selected as the reference model to describe the required speed trajectory. To make the actual speed of the PMSM-VSD system follow this trajectory, the proposed STSMO-MRA-SC comprises three terms: (1) the stabilization term dependent on known parameters of the motion dynamics and the selected reference model for stabilizing the speed tracking error dynamics asymptotically; (2) the disturbance compensation term based on the STSMO for compensating the lumped disturbance in the speed tracking error dynamics; and (3) the error compensation term updated online by the adaptive law for confronting the estimation error of the STSMO in practice. Comparative experimental tests among the classic MRA-SC, the radial basis function neural network-based MRA-SC and the proposed STSMO-MRA-SC are performed. Experimental results have verified the effectiveness and the superiority of the proposed STSMO-MRA-SC.

Online Learning of Minmax Solutions for Distributed Estimation and Tracking Control of Sensor Networks in Graphical Games

In this article, a new target tracking algorithm that is based on a distributed estimation-based control protocol is developed for multiple moving sensors subject to adversarial inputs. An augmented system composed of both the estimation error dynamics and the tracking error dynamics is introduced for the distributed estimation and target tracking control problem. We integrate estimation and control to simultaneously minimize infinite-horizon estimation and tracking errors in sensor networks with disturbances. A Minmax strategy as an alternative goal to Nash equilibrium is proposed to compute the sensor’s optimal motion controls in the presence of worst-case neighbor controls and disturbances. In contrast to Nash, Minmax yields a distributed algebraic Riccati equation that is easily solved locally by each sensor. A method based on reinforcement learning is given to compute sensor motion inputs so that all sensors estimate and track the target states. Value function approximation using neural networks is used to solve the distributed Bellman equations online based on the real-time observed data. Proofs are given to guarantee the performance of the combined distributed estimation and tracking algorithms. Finally, the simulation examples show the effectiveness of the proposed algorithm.

Optimal Consensus Control Design for Multiagent Systems With Multiple Time Delay Using Adaptive Dynamic Programming.

In this article, a novel data-based adaptive dynamic programming (ADP) method is presented to solve the optimal consensus tracking control problem for discrete-time (DT) multiagent systems (MASs) with multiple time delays. Necessary and sufficient conditions of the corresponding equivalent time-delay system are provided on the basis of the causal transformations. Benefitting from the construction of tracking error dynamics, the optimal tracking problem can be transformed into settling the Nash-equilibrium in the graphical game, which can be completed by solving the coupled Hamilton-Jacobi (HJ) equations. An error estimator is introduced to construct the tracking error of the MASs only using the input and output (I/O) data. Therefore, the designed data-based ADP algorithm can minimize the cost functions and ensure the consensus of MASs without the knowledge of system dynamics. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

쿼드로터 UAV 의 PPO 기반 모델 참조 추종 제어

This paper presents a proximal policy optimization (PPO)-based model reference tracking controller design for quadrotor unmanned aerial vehicles (UAVs). First, the quadrotor UAV is divided into the attitude and position systems, and each system is expressed as a nonlinear state-space equation. Thereafter, we design a linear reference model, which is used to derive the tracking error dynamics. The proposed neural network model implements a PPO-based reinforcement learning algorithm consisting of an actor approximating a policy and a critic corresponding to a state-value function. The actor receives the state variables of the tracking error dynamics as input and outputs the thrust values to be applied to each axis. Further, we decentralize the PPO-based controller into the attitude and position controllers, which are then trained separately. For learning purposes, we implement an environment code that expresses the tracking error dynamics of the quadrotor by extending the OpenAI Gym environment. Finally, a simulation example is provided to show the position tracking performances of up to 0.0166 m and 0.0254 m for the horizontal and vertical axes, respectively.

Disturbance observer-based nonfragile fuzzy tracking control of a spacecraft

This paper deals with the nonfragile fuzzy tracking control technique of a spacecraft subject to external disturbances and control gain uncertainties. First, the Takagi–Sugeno (T–S) fuzzy model of the tracking error dynamics is newly derived. Unlike the existing studies, we assume that the controller output is norm bounded and its gain matrix is perturbed because of the aging of the actuator. Next, a fuzzy disturbance observer (DOB) estimating the external disturbance is constructed to enhance the robustness of the control system. Then, a fuzzy controller feeding back the estimated disturbance is designed to attenuate external disturbances. In addition, we establish the linear matrix inequality (LMI) conditions, by which both the H∞ disturbance attenuating performance and the asymptotic stabilization are guaranteed. From the solution to the LMI conditions, we obtain the controller and DOB gain matrices. Finally, a simulation example validates the disturbance estimation and tracking performance of the proposed method.

Fault-tolerant tracking control for nonlinear observer-extended high-order fully-actuated systems

In the paper, a fault-tolerant tracking control strategy is proposed for a class of nonlinear high-order fully-actuated systems (HOFASs) with multiplicative and additive actuator faults. Different from general state space methods, HOFAS approaches can achieve global stability through specific nonlinear control laws, and maintain the fully-actuated and uncoupled characteristics of most physical objects. Starting from the HOFAS tracking error dynamics, a tracking differentiator is designed to solve the reference signal and its derivatives numerically. Furthermore, a specific extended state observer is firstly embedded into the HOFAS, which expands the application scenarios of the HOFAS theory. Based on Lyapunov stability theory, a fully-actuated fault-tolerant control technique is presented to ensure the uniformly ultimately bounded stability of the tracking error. A numerical comparative experiment fully illustrates the effectiveness of the proposed strategy.

Dynamic Tube Model Predictive Control for Powered-Descent Guidance

In this paper, a dynamic tube nonlinear model predictive control (NMPC) scheme is developed to solve the powered-descent guidance (PDG) problem in the presence of bounded disturbances and no-fly zones. First, owing to its simplicity and robustness, time-varying boundary layer sliding mode control (SMC) is used as an ancillary controller to compensate for external disturbances. Consequently, the tube geometry dynamics can be established as first-order differential equations to calculate the robust control invariant tube. Hence, the nominal trajectory and tube geometry are optimized simultaneously to improve the control performance by augmenting the tube geometry dynamics in open-loop MPC optimization. Moreover, the tube can be shrunk to reduce the conservativeness and enhance optimization feasibility by exploiting the tube geometry and tracking error dynamics. In addition, a constraint-tightening method is employed to ensure that the PDG problem satisfies all the constraints while accounting for the uncertainty caused by the disturbance. Finally, numerical case studies and Monte Carlo simulations validate the effectiveness and performance of the proposed strategy.

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.

Passivity-based controller for charging of Lithium-ion battery model 18650

This article deals with a lithium-ion battery charger using a passivity-based controller (called: the exact tracking error dynamics passive output feedback (ETEDPOFC)), which uses the constant-current constant-voltage (CC-CV) protocol. For this, the charger system consists of 3 phases. The first phase involves designing the dc-dc buck power converter, considering the operating voltage and maximum current the battery can withstand—where the passivity-based control operates in the balance points proposed as a function of the load protocols. The second phase consists of the general PSIM simulation of the system (converter + battery), which uses the Shepherd model to characterize the battery used in the tests. Finally, the third phase shows the implementation based on the system’s TMS320F28335 card DSP, just like the experimental results.