Tracking Controller Design Method Research Articles

Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

<p>In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.</p>

New LADRC scheme for fractional-order systems

Active Disturbance Rejection Control (ADRC) is a very promising recent concept for the design of controllers to control systems with uncertainties. Based on an extended state observer, this control structure allows both external disturbances and modeling uncertainties to be actively rejected. The use of the active rejection control of disturbances is gaining more and more interest among the system control community. This is mainly due to its easy design, undemanding implementation and robustness. In this paper, three solutions using the ARDC structure to control fractional-order system are discussed. Two methods taken from the literature are briefly introduced, namely, the fractional-order dynamics rejection scheme (FODRS) and the fractional linear active disturbance rejection control (FLADRC). The basic ideas and technical formulations of these two are presented. A third method, based on the robustness performance introduced by fractional-order controllers, is also proposed in this paper. The proposed design method of the set-point tracking controller is based on the Bode’s ideal transfer function (Bode’s ITF). This will improve the robustness of the control scheme.

Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework

We present a trajectory tracking control design method for a class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on the virtual contractivity-based control (v-CBC) method, which employs the notions of virtual systems and of contractivity. This approach leads to a family of asymptotic tracking controllers that are not limited to those that preserve the pH structure of the closed-loop system nor require an intermediate change of coordinates. Nevertheless, structure preservation and other properties (e.g., passivity) are possible under sufficient conditions. The performance of the proposed v-CBC scheme is experimentally evaluated on a planar robot of two degrees of freedom (DoF).

Finite-time optimal tracking control using augmented error system method

This paper proposes a design method of finite-time optimal tracking controller for quadratic performance index. A novel nonlinear finite-time optimal controller is designed to solve the finite-time optimal tracking control problem for linear system. By applying augmented error system method and finite-time optimal state feedback control, sufficient conditions involving V-function are obtained, and eventually, a nonlinear controller based on the V-function is derived. In addition, the construction of a specific V-function satisfying those conditions is discussed in detail. The nonlinear controller which we introduced makes closed-loop system finite-time stable, so that the tracking error of original system converges in finite time. The simulation example illustrates the efficiency of our results.

시간지연을 갖는 2축 짐벌시스템의 강인한 추종제어계 설계에 관한 연구

This paper presents a novel target tracking control design method for 2-axis gimbal system. Especially, the delay time raised from control signal calculation, sensing signal transducing and transmitting, affects the system stability and degrades the control performance. To overcome these issues, in this study, the authors propose a new tracking system design method based on robust control framework. The designed control system can preserve the system stability and control performance simultaneously in spite of time delay. The developed control method was applied to a 2-axis gimbal system. A STSMC (super-twisting sliding mode control) scheme was provided for a comparison study. Finally, the simulation results were presented for validating the usefulness of the method.

Decentralized sampled-data fuzzy controller design for a VTOL UAV

This study focuses on a sampled-data fuzzy decentralized tracking control problem for a quadrotor unmanned aerial vehicle (UAV) under the variable sampling rate condition. To this end, the overall dynamics of the quadrotor is expressed as a decentralized Takagi–Sugeno (T–S) fuzzy model interconnected with each other. Although the proposed decentralized control technique divides the overall UAV control system into attitude and position subsystems, the stability of the entire control system is guaranteed. Besides, in this paper, the model uncertainty, interconnection, and reference trajectory are considered as disturbances acting on the tracking error. To attenuate these disturbances, a novel sampled-data tracking control design technique is derived based on a linear reference model to be tracked and the time-dependent Lyapunov–Krasovskii functional (LKF). By doing so, both the stability of the tracking error dynamics and the minimization of tracking performance are guaranteed. Also, the proposed tracking control design method is derived as a linear matrix inequality (LMI)-based optimal problem. Finally, a simulation example is provided to demonstrate the effectiveness and feasibility of the proposed design methodology.

Safe Tracking Control of an Uncertain Euler-Lagrange System with Full-State Constraints using Barrier Functions.

This paper presents a novel, safe tracking control design method that learns the parameters of an uncertain Euler-Lagrange (EL) system online using adaptive learning laws. A barrier function (BF) is first used to transform the full-state constrained EL-dynamics into an equivalent unconstrained dynamics. An adaptive tracking controller is then developed along with the parameter update law in the transformed state space such that the states remain bounded for all time within a prescribed bound. A stability analysis is developed that considers the EL-dynamics' uncertainty, yielding a semi-globally uniformly ultimately bounded (SGUUB) tracking error and the parameter estimation error. The controller design is validated in simulations using a two-link planar manipulator. The results show the proposed method's ability to track the reference trajectory while remaining inside each of the predefined state bounds.

Output Tracking and Feedback Controller Design for Nonlinear Stochastic Time-Delay System

This paper considers the design of output tracking and feedback controllers for nonlinear stochastic systems. The system status cannot be measured. The studied system contains nonlinear state functions, noise disturbances and time delays. We use the free weight matrix method to avoid the conservatism caused by the use of model transformation or cross-term bounded techniques. Based on the Lyapunov-Krasovskii functional method, we propose an output tracking and feedback controller design method based on linear matrix inequality (LMI). Numerical examples show the validity of the obtained results.

Observer‐based tracking controller design for a class of polynomial fuzzy systems with disturbance

AbstractIn this paper, the tracking control law design problem for a class of polynomial fuzzy systems subjected to external bounded disturbance is studied. The tracking control design problem is solved using the observer‐based tracking controller design method in which the observer estimates the controlled system state vector and also the system states will follow the state vector of a stable reference model subject to an H∞ performance. The process of calculating controller parameters is formulated as an SOS feasibility program. Simulation results are presented to show the merits of the proposed control design approach.

Active Disturbance Rejection Based Robust Trajectory Tracking Controller Design in State Space

This paper proposes a new active disturbance rejection (ADR) based robust trajectory tracking controller design method in state space. It can compensate not only matched but also mismatched disturbances. Robust state and control input references are generated in terms of a fictitious design variable, namely differentially flat output, and the estimations of disturbances by using differential flatness (DF) and disturbance observer (DOb). Two different robust controller design techniques are proposed by using Brunovsky canonical form and polynomial matrix form approaches. The robust position control problem of a two mass-spring-damper system is studied to verify the proposed ADR controllers.

A Novel Neural-Network-Based Adaptive Control Scheme for Output-Constrained Stochastic Switched Nonlinear Systems

In this paper, a novel neural-network (NN)-based adaptive tracking controller design method is presented for the single-input/single-output nonlinear stochastic switched systems in lower triangular structures with an output constraint. First, a well-designed nonlinear mapping is introduced to transform the switched stochastic system to a new system without constraints, which implies the controller design of the transformed system is equivalent to that of the stochastic switched system. Then radial basis function NNs are applied to model the unknown nonlinearities and the adaptive backstepping technique is employed to construct two classes of adaptive neural controllers under different adaptive laws. It is proved that both controllers can assure all the signals in the closed-loop remain bounded in probability, and the tracking error finally converges to a neighborhood of the origin without violating the constraint. Furthermore, the use of the nonlinear mapping to deal with the asymmetric output constraint is also studied as a generalization result. Two illustrative examples with numerical data and simulation results are given to show the validity and performance of the proposed control schemes.

Tracking Control of Networked Multiple Linear Switched Reluctance Machines Control System Based on Position Compensation Approach

This paper proposes the precise tracking control for the multiple linear switched reluctance machines (LSRMs) with network-induced time delays by using the motor positions compensation method. Considering the mutual position disturbances among the multiple motors, two network topologies are proposed for the multiple LSRMs control system. In order to improve the tracking precision, the motor position signals are used to compensate the tracking errors among the three motors. The encoders-to-controller and the controller-to-actuator time delays are modeled as a discrete-time Markov chain which denotes the whole random time delay step for the closed-loop control system. The stability conditions and the tracking controller design method for the networked LSRMs control system are proposed by using Lyapunov theory and the inequality techniques. Several groups of experimental results are presented to verify the effectiveness and practicability of the proposed method for the networked multiple LSRMs control system.

Point-to-Point Iterative Learning Control With Optimal Tracking Time Allocation

Iterative learning control (ILC) is a high-performance tracking control design method for systems operating in a repetitive manner. This paper proposes a novel design methodology that extends the recently developed point-to-point ILC framework to allow automatic via-point time allocation within a given point-to-point tracking task, leading to significant performance improvements, e.g., energy reduction. The problem is formulated into an optimization framework with via-point temporal constraints and a reference tracking requirement, for which a two-stage design approach is developed. This yields an algorithmic solution, which minimizes input energy based on norm optimal ILC and gradient minimization. The algorithm is further expanded to incorporate system constraints into the design, prior to experimental validation on a gantry robot test platform to confirm its feasibility in practical applications.

Retrofit fault‐tolerant tracking control design of an unmanned quadrotor helicopter considering actuator dynamics

SummaryThis paper presents a retrofit fault‐tolerant tracking control (FTTC) design method with application to an unmanned quadrotor helicopter (UQH). The proposed retrofit fault‐tolerant tracking controller is developed to accommodate loss‐of‐effectiveness faults in the actuators of UQH. First, a state feedback tracking controller acting as the normal controller is designed to guarantee the stability and satisfactory performance of UQH in the absence of actuator faults, while actuator dynamics of UQH are also considered in the controller design. Then, a retrofit control mechanism with integration of an adaptive fault estimator and an adaptive fault compensator is devised against the adverse effects of actuator faults. Next, the proposed retrofit FTTC strategy, which is synthesized by the normal controller and an additional reconfigurable fault compensating mechanism, takes over the control of the faulty UQH to asymptotically stabilize the closed‐loop system with an acceptable performance degradation in the presence of actuator faults. Finally, both numerical simulations and practical experiments are conducted in order to demonstrate the effectiveness of the proposed FTTC methodology on the asymptotic convergence of tracking error for several combinations of loss‐of‐effectiveness faults in actuators.

Asymptotic Fuzzy Tracking Control for a Class of Stochastic Strict-Feedback Systems

This paper presents an asymptotic tracking control design method for stochastic strict-feedback systems via fuzzy logic systems. In the existing results, stochastic controls are usually limited to be bounded in probability. However, how to realize the asymptotic tracking control for stochastic strict-feedback systems remains a control dilemma. This paper achieves the asymptotic tracking control by proposing a novel gain suppressing inequality approach. Specifically, the three-part construction is performed to achieve such control objective for stochastic systems. First, the novel gain suppressing inequality technique is developed to lay the foundation for carrying out the Lyapunov stability analysis. Second, the developed inequality technique is integrated with each step of the backstepping-based adaptive control design procedure. Third, analyses are provided to realize the asymptotic tracking control of stochastic strict-feedback systems.

Adaptive Fuzzy Decentralized Control for a Class of Large-Scale Nonlinear Systems With Actuator Faults and Unknown Dead Zones

This paper studies the fault-tolerant control problem for a class of uncertain large-scale nonlinear systems with unknown dead zones and actuator failures, including outage, loss of effectiveness, and stuck. It is assumed that the lower and upper bounds of actuator efficiency factor, the unparametrizable time-varying stuck fault, the system coefficient, and the uncertain functions of our considered systems are unknown. By introducing a smooth function, fuzzy logic systems and a bound estimation approach, a decentralized backstepping design method of fault-tolerant tracking controller is developed for the systems under consideration. The proposed controller can compensate the effects of actuator faults and dead zones completely. It is proved that all the signals in the closed-loop systems are ultimately bounded, and the tracking control performance can be achieved by the proposed controller. In comparing with the existing results, the restrictions on the number of failures are removed and the stuck fault is allowed to be time-varying. Finally, simulation results show the efficiency of the proposed control scheme.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Multiple models decentralized coordinated control of doubly fed induction generator

• The correlative measured model of doubly feed induction generator is obtained. • A multiple model optimal tracking control based on correlative measured model is proposed. • The obtained control law can be considered as a decentralized coordinate control. • Various disturbances were applied in a hybrid power system to illustrate the contributions. In this paper, a multiple model optimal tracking control (MOTC) design method for the double fed induction generator (DFIG) using correlative measured technique is proposed. The DFIG is represented by a third-order model, where electro-magnetic transients of stator are neglected. By using the correlative measured technique, the correlative measured matrix (CMM) of wind power system is obtained firstly. Then, a nonstandard state space equation of DFIG is obtained with the correlative measured vectors (CMVs), which reflect interactions between the DFIGs and grid. In order to cope with nonlinearities and continuous variation in the operating points, a multiple model design method is proposed in the discrete domain. The obtained control law, synthesized by using Bayesian probability, only depends on the local measured parameters. Hence, the MOTC can be regarded as a decentralized coordinated control, which can simplify the control structure and improve the transient stability of DFIG. To illustrate the effectiveness of the proposed MOTC strategy, simulations on a hybrid wind thermal power (HWTP) system are performed. The results show that the proposed MOTC strategy can provide acceptable performance throughout the whole operating region. Comparing to the conventional PID control, transient stability, damping, and fault ride-through capability of DFIG with the proposed MOTC design method have been improved effectively.

Robust Adaptive Fault-Tolerant Tracking Control of Three-Phase Induction Motor

This paper deals with the problem of induction motor tracking control against actuator faults and external disturbances using the linear matrix inequalities (LMIs) method and the adaptive method. A direct adaptive fault-tolerant tracking controller design method is developed based on Lyapunov stability theory and a constructive algorithm based on linear matrix inequalities for online tuning of adaptive and state feedback gains to stabilize the closed-loop system in order to reduce the fault effect with disturbance attenuation. Simulation results reveal the merits of proposed robust adaptive fault-tolerant tracking control scheme on an induction motor subjected to actuator faults.

Disturbance-Observer-Based Robust H∞Switching Tracking Control for Near Space Interceptor

A novel robust <TEX>$H_{\infty}$</TEX> switching tracking control design method with disturbance observer is proposed for the near space interceptor (NSI) with aerodynamic fins and reaction jets. Initially, the flight envelop of the NSI is divided into small subregions, and a slow-fast loop polytopic linear parameter varying (LPV) model is proposed, to approximate the nonlinear dynamic of the NSI, based on the Jacobian linearization and Tensor-Product (T-P) model transformation approach. A disturbance observer is then constructed, to estimate the modeled disturbance. Subsequently, based on the descriptor system method, a robust switching controller is developed, to ensure that the closed-loop descriptor system is stable with a desired <TEX>$H_{\infty}$</TEX> disturbance attenuation level. Furthermore, the outcome of the proposed switching tracking control problem is formulated as a set of linear matrix inequalities (LMIs). Finally, simulation results demonstrate the effectiveness of the proposed design method.