Adaptive and Robust Fault-Tolerant Tracking Control of Contact force of Pantograph-Catenary for High-Speed Trains

Abstract This paper presents a modified multi-body dynamic model and a linear time-invariant model with actuator faults (loss of effectiveness faults, bias faults) and matched and unmatched uncertainties. Based on the fault model, a class of adaptive and robust tracking controllers are proposed which are adjusted online to tolerate the time-varying loss of effectiveness faults and bias faults, and compensate matched disturbances without the knowledge of bounds. For unmatched uncertainties, optimal control theory is added to the controller design processes. Simulations on a pantograph are shown to verify the efficiency of the proposed fault-tolerant design approach

Adaptive Actuator Compensation of Position Tracking for High-Speed Trains with Disturbances

In this paper, the adaptive fault compensation prob-lem is investigated for high-speed trains in the presence of time-varying system parameters, disturbances and actuator failures. To deal with the time-varying system parameters, a new time-varying indicator function instead of commonly used 0-1 function, is proposed to model the train dynamics as a piecewise model with unparameterizable time-varying disturbances, which can cover more time variations and help parametrization for adaptation. A backstepping adaptive controller is designed for the healthy system with unknown piecewise model parameters and known piecewise bounds on disturbances. For both the parameterizable and unparameterizable failures, the backstepping adaptive fail-ure compensation with the adaptive laws are derived to achieve the position tracking under the known bound disturbances. The adaptive failure compensation for unknown bounds on disturbances is also discussed under the parameterizable failure. Through introducing the nonlinear damping in the proposed controller, the failure compensation controller is proposed for the model with unparameterizable system parameters to achieve an arbitrary degree of position tracking accuracy. The stability of the corresponding closed-loop system and asymptotic state tracking are proved via Lyapunov direct method, and validated using a high-speed train model

Adaptive Control Design and Evaluation for Multibody High-speed Train Dynamic Models

In this paper, the adaptive tracking control problem is investigated for multibody high-speed train dynamic model in the presence of unknown parameters, which is an open adaptive control problem. A 4-car train unit model with input signals acting on the 2nd and 3rd cars and output signals being the speeds of the 1st and 3rd cars is chosen as a benchmark model, in which the aerodynamic resistance force is also considered. To handel the nonlinear term, the feedback linearization method is employed to decompose the system into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is Lyapunov stable and is also partially input-to-state stable under the condition that the speed error between the 1st and 3rd cars is exponentially convergent (to be ensured by a nominal controller) or belongs to the L1 signal space (to be achieved by a properly designed adaptive controller). The system configuration leads to a relative degree 1 subsystem and a relative degree 2 subsystem, for which different feedback linearization-based adaptive controllers and their nominal versions are developed to ensure the needed stabilization condition, the desired closed-loop system signal boundedness and asymptotic output speed tracking. Detailed closed-loop system stability and tracking performance analysis are given for the new control schemes. Simulation results from a realistic train dynamic model are presented to verify the desired adaptive control system performance

Decentralised sliding mode control for nonlinear interconnected systems in the regular form

In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems in regular form. All the isolated subsystems and interconnections are fully nonlinear. It is not required that the nominal isolated subsystems are either linearizable or partially linearizable. The uncertainties are nonlinear and bounded by nonlinear functions. Specifically, uncertainties in the input distribution and interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed by only employing local information. Sufficient conditions are developed under which information on the interconnections is employed for decentralised controller design to reduce conservatism. The bounds on the uncertainties have more general forms compared with previous work. A simulation example is used to demonstrate the effectiveness of the proposed method

Stabilisation of Time Delay Systems with Nonlinear Disturbances Using Sliding Mode Control

This paper focuses on a class of control systems with delayed states and nonlinear disturbances using sliding mode techniques. Both matched and mismatched uncertainties are considered which are assumed to be bounded by known nonlinear functions. The bounds are used in the control design and analysis to reduce conservatism. A sliding function is designed and a set of sufficient conditions is derived to guarantee the asymptotic stability of the corresponding sliding motion by using the Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesised to drive the system to the sliding surface in finite time and maintain a sliding motion thereafter. Effectiveness of the proposed method is demonstrated via a case study on a continuous stirred tank reactor system

Variable structure observer for a class of nonlinear large-scale interconnected systems with uncertainties

In this paper, a variable structure observer design approach is proposed for a class of nonlinear, large-scale interconnected systems in the presence of unstructured uncertainty. The modern geometric approach is exploited to explore the system structure and a transformation is developed to facilitate observer design. Using the Lyapunov direct method, a robust asymptotic observer is presented which exploits the internal dynamic structure of the system as well as the structure of the uncertainties. The bounds on the uncertainties are nonlinear and are employed in the observer design to reject the effect of the uncertainties. A numerical example is presented to illustrate the approach and the simulation results show that the proposed approach is effective

Fault-Tolerant Control for Systems with Unmatched Actuator Faults and Disturbances

A fault-tolerant control (FTC) scheme for a class of nonlinear systems with unmatched actuator redundancy and unmatched disturbances is proposed in this note. A methodology to construct unified smooth sliding mode control laws and update laws is proposed such that the equivalent injections of the first-order time derivatives of the unmatched actuator faults and unmatched disturbances can appear in the unmatched channels. The unmatched actuator faults and unmatched disturbances are completely canceled by these equivalent injections. Based on this methodology and using the backstepping design procedure, a set of smooth FTC sliding surfaces, FTC laws and update laws are then designed. With the help of the FTC law selecting mechanism, the output tracking errors of the closed-loop FTC system converge to zero asymptotically, and time-varying faults and disturbances are reconstructed. A simulation example is presented to illustrate the effectiveness of the proposed FTC method

Incipient Voltage Sensor Fault Isolation for Rectifier in Railway Electrical Traction Systems

This paper proposes a dc voltage incipient sensor fault isolation method for single-phase three-level rectifier devices in high-speed railway electrical traction systems. Different incipient fault modes characterizing locations and incipient fault types are parameterized nonlinearly by unknown fault parameters. A new incipient fault isolation method is developed by combining sliding mode technique with nonlinear parametrization adaptive estimation technique. A bank of particular adaptive sliding mode estimators is proposed, which facilitates to derive new isolation residuals and adaptive threshold intervals. The isolability is studied, and the isolable sufficient condition is derived using new functions. For the practical electrical traction system in CRH2 (China Railway High-Speed 2), simulation and experiment based on TDCS-FIB (a software) are presented to verify the effectiveness and feasibility of the proposed method

Adaptive Compensation of Traction System Actuator Failures for High-Speed Trains

In this paper, an adaptive failure compensation problem is addressed for high-speed trains with longitudinal dynamics and traction system actuator failures. Considered the time-varying parameters of the train motion dynamics caused by time-varying friction characteristics, a new piecewise constant model is introduced to describe the longitudinal dynamics with variable parameters. For both the healthy piecewise constant system and the system with actuator failures, the adaptive controller structure and conditions are derived to achieve the plant-model matching. The adaptive laws are designed to update the adaptive controller parameters, in the presence of the system piecewise constant parameters and actuator failure parameters which are unknown. Based on Lyapunov functions, the closed-loop stability and asymptotic state tracking are proved. Sim-ulation results on a high-speed train model are presented to illustrate the performance of the developed adaptive actuator failure compensation control scheme

Zero Dynamics Analysis and Adaptive Tracking Control of Underactuated Multibody Systems with Flexible Links

This paper studies the adaptive tracking control problem for underactuated multibody systems with flexible links in the presence of unknown parameters. A four-body system with input signals acting on the first and fourth bodies is chosen as a benchmark model, which can be decomposed into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is Lyapunov stable and is partially input-to-state stable under the condition that the speeds of first and fourth bodies are synchronous. The physical meaning of such partial input-to-state stability is clarified. An adaptive controller is developed to ensure such a needed system stabilization condition and thus the boundedness of the desired closed-loop system signal and asymptotic speed tracking of the control dynamics subsystem. Detailed closed-loop system stability and tracking performance analysis are given, in which the tracking errors satisfy the L^1 performance. Extensions to the other multibody systems with flexible links are derived. The developed adaptive controller is applied to a realistic train dynamic model, and simulation results verify the desired system performance