Exact Input-output Linearization Research Articles

Development of a Motion Control for a highly dynamic, self-propelled driving simulator

The new concept of the self-propelled driving simulator comprises a hexapod, a yaw joint and a wheel-based motion platform with four individually steerable wheels. This concept provides a theoretically unlimited motion range, which especially enables highly dynamic drive maneuvers. To ensure an omnidirectional motion, the motion platform has to accelerate instantly in any direction. This requirement leads to the main challenges in the control system of the simulator: taking into account the nonlinear and transient tire characteristics and generating the target accelerations as expected by the driver. According to these requirements, the Motion Control is only for controlling the horizontal dynamics of the motion platform. The Motion Control presented in this paper includes various model definitions, especially regarding the essential tire characteristics considered within an extended HSRI (Highway Safety Research Institute) tire model. The Motion Control as Two-Degrees-of-Freedom control contains a Feedforward for generating target body forces, a Control Allocation for an optimal force distribution to the wheels, a Single Wheel Control as a specific control of the tire forces, and a Compensation Control on acceleration level. Investigation of this control by simulation, using a simplified reference model, already revealed a high controller performance regarding accuracy and quality. The optimal force distribution leads to an equal adhesion utilization and the Compensation Control compensates the remaining Single Wheel Control deviations. Difficulties only occur for the steering angle in the case of low velocity up to a standstill. Due to the exact input–output linearization, the Single Wheel Control leads to a singularity and instability. Therefore, the steering angle requires exceptional control in this case.

The Dynamics Characteristics of Flexible Spacecraft and its Closed-Loop Stability with Passive Control

Passive control is the most popular methodology for flexible spacecraft while it remains an open problem whether the closed-loop performance can be achieved only with passive control subject to the coupling modes of rigid and flexibility. Also, the closed-loop performance of passive PD control based on the dynamics of the Euler angle parameterization of spacecraft, which has been widely used in practice, is yet to be addressed. Towards these challenges, by introducing the input-output exact linearization theory and Lyapunov theory, the authors show that the closed-loop performance for flexible spacecraft with rigid and flexible modes can be achieved by adjusting the parameters of the passive controllers sufficiently large. This is done by firstly transforming the flexible spacecraft dynamics into an exact feedback linearization standard form, and then analyzing the closed-loop performance of flexible spacecraft.

Feedback Linearization Based Direct Torque Control for IPMSMs

A feedback linearization based direct torque control (FL-DTC) scheme is designed for interior permanent magnet synchronous motors drives. Several main aspects related to FL are studied thoroughly. A proper choice of two new state variables (the torque and the squared amplitude of stator flux) yields the exact input-output linearization decoupling of the closed-loop system. The FL-DTC frame is obtained after finding a feasible diffeomorphism. For the partially linearized subsystem, i.e., the independent torque and flux loops, two FL-DTC-based controller design solutions are provided. The control problem of internal dynamics is converted to an absolute tracking problem of an equivalent Lur'e system.

Design of a central feedforward control of torque vectoring and rear-wheel steering to beneficially use tyre information

ABSTRACT This paper presents the design of a central feedforward control for the two chassis control systems rear-wheel steering (RWS) and torque vectoring (TV) which have related areas of intervention in lateral dynamics. A control strategy is presented in order to follow desired target values consisting of yaw acceleration and sideslip angle velocity. Central attention is given to the use of additional tyre information with the aim of enhancing vehicle handling and stability. With the knowledge of the mounted tyre type, an adaption law for the desired target values is derived. Although the focus is based on the usage of new tyre information, this modelling approach basically has the potential to reduce the need for coordination among the two systems RWS and TV, exploiting the synergies between both of them. Starting from an extended single-track model an exact Input–output linearisation method is used to design the feedforward control. This is followed by a proof of stability for the external and the internal dynamics of the controller. For the subsequent investigation, in a preliminary step, real-world in vehicle tests are carried out under varying tyre types with a wide spreading of characteristics. This serves as a basis to identify the most important tyre parameters for the controller and to derive the target goals. Finally, the controller is implemented in a 14-DOF non-linear entire vehicle model in Matlab/Simulink, that serves for simulations with a virtual vehicle plant. The performance of the presented feedforward control is assessed by specified objective criteria for steady-state and transient open-loop manoeuvres in lateral dynamics. These criteria are used to investigate the effectiveness of the control design with the aim to achieve the defined target motion. In addition to that, the manoeuvre results also serve to evaluate the control effort, involved in the coordinated cooperation of both systems.

A novel approach for dynamic gas conditioning for PEMFC stack testing

The air supply to the polymer electrolyte membrane fuel cell (PEMFC) stack is crucial for the performance of a PEMFC system. To enable modular and transient testing of the stack during development, a novel dynamic gas conditioning system is presented. To meet the requirements of transient stack testing, different hardware concepts for the testbed are evaluated and an experimental setup is realised. The thermodynamic states of this system are coupled through various relations and represent a nonlinear multivariate control problem. For controller design a dynamic nonlinear model of the system is derived and parameterised with measurements from the testbed. To decouple the system and achieve a good transient response the model-based nonlinear control concept of exact input-output linearisation is applied. Based on the decoupled system, a Two-Degree-of-Freedom (2DoF) controller is designed. The application of this nonlinear control concept on the realised hardware setup shows that accurate trajectory tracking during dynamic set point changes is ensured. Experimental results are presented to validate the control performance.

Flatness-based feedforward control of polymer electrolyte membrane fuel cell gas conditioning system

Manufacturers of automotive applications rely on high-performance testing environments for the development of polymer electrolyte membrane fuel cell (PEMFC) technologies. The main component of a PEMFC testbed is the gas conditioning system, which controls the inlet gas temperature, stack pressure, relative humidity and mass flow of the gas at the inlet of the PEMFC stack. This paper presents a control concept for a highly dynamic PEMFC gas conditioning system. The main control challenge lies in the decoupling of the governing thermodynamic quantities. Therefore, the nonlinear control concept of exact input–output linearisation with an extended PID control structure is applied. Constraints on the actuators are incorporated by formulating the resulting control law as an optimisation problem. The robustness with respect to parameter uncertainties for the model is shown by investigating the trajectory tracking error of the disturbed system. Simulation results show an overall good performance for the trajectory tracking and demonstrate the robustness of the model against parameter uncertainties.

Adaptive tracking control of quad-rotor helicopter in quaternion based on input-output linearisation with online estimation of inertia moment

In this paper, we consider problems of controlling the position of a quad-rotor helicopter in the quaternion. The quad-rotor helicopter is described by a set of nonlinear equations, which make it difficult to control. This paper presents a useful exact input-output linearisation in the quaternion of the helicopter by using a non-singular input transformation. This linearisation provides both simple controller designs and higher level control performance, for example, the H-infinity control. In addition, this paper presents an adaptive tracking controller with online estimation of the uncertain inertia parameters to make the tracking error zero asymptotically for the position.

Constraint mapping in a feedback linearization/MPC scheme for trajectory tracking of underactuated multibody systems

In this work, a nonlinear control scheme consisting of an exact feedback linearization and a model predictive controller is presented in order to track reference trajectories for an end-effector of an underactuated multibody system. In the case of minimum-phase systems, designing a feedback linearization results in an exactly linearized system, which can be used for model predictive control design. A method is proposed in detail how to handle mechanical constraints like restricted inputs through the nonlinear mapping of the feedback linearization in the optimization problem. A predictive controller combined with an exact input-output linearization is applied to a serial manipulator with a passive joint, which enables both accurate trajectory tracking and compliance of the constraints.

Stabilization of non-minimum phase switched nonlinear systems with the concept of multi-diffeomorphism

In this paper we propose a control approach for the stabilization of a class of switched nonlinear systems where each mode may be non-minimum phase. The proposed approach is based on the exact input–output linearization and the Lyapunov stability theory. The main contribution in this work is to elaborate a strategy of switching that recourse to the concept of multi-diffeomorphism makes it possible to guarantee an improvement of the transient state compared to a feedback linearization based on one diffeomorphism. Specifically, we show the sufficient condition for the exponential stability and the exponential upper bound of the trajectory of the switched system. The theoretical results are applied to a non-minimum phase inverted cart–pendulum in order to illustrate the effectiveness of the proposed approach.

Sensorless Exact Input-Output Linearization Control of the Induction Machine, Based on Parallel Stator Resistance and Speed MRAS Observer, with a Flux Sliding Mode Observer

Abstract: This paper presents an exact input-output linearization control scheme for rotor speed and rotor flux control of induction motor drive. In this scheme the motor model, is described in the fixed stator frame, and it is linearized, using exact inputoutput linearization technique, allowing a decoupled control of rotor flux and torque. To avoid the use of mechanical sensor, the rotor speed estimation is made by an observer using a specific MRAS (Model reference adaptive system) technique; this observer is designed to perform simultaneous estimation of stator resistance and rotor speed. In order to estimate rotor flux, a sliding mode observer is proposed in this paper. Simulation results are realized and presented to validate and to prove the effectiveness of the proposed Sensorless control.

On the coordinated control of multiple HVDC links using input–output exact linearization in large power systems

Stability of power systems may limit the amount of transfer capacity between areas as the systems tend to be more utilized. The controllability brought by the high voltage direct current (HVDC) links is a possible access to increase the stability and thereby the power transfer. The main contribution of this article is a coordinated control strategy for multiple HVDC links to improve both transient and small signal stability. The input–output exact feedback linearization is used to map the nonlinear system model to a linear model seen from the input to the output. Linear control design can now be used, such as the linear quadratic regulator (LQR). This linearization is not the commonly used Taylor linearization, the input–output exact feedback linearization cancels the nonlinearities by a pre-feedback loop. An extension of the internal node representation by including the dynamics of the HVDC links in the nonlinear differential swing equations is also developed, which is needed for the feedback control design.

Modified non-linear damping of internal dynamics via feedback linearisation for static synchronous compensator

Static synchronous compensator (STATCOM) is a non-linear system so that the conventional linear output feedback controller with synthesised feedback control cannot guarantee uniform tracking performance, although it improves the stability margin in an inductive operating range. Recently, the input-output linearisation via feedback has been applied to STATCOM and it shows uniform transient performance but owing to lightly damped internal dynamics it results in current ripples in DC-side capacitors. To reduce the ripples, a damping term, time derivative of active current multiplied by a constant gain, was added to the input-output linearisation. This damping controller brings improved internal stability by moving the poles of internal dynamics from the imaginary axis. However, there exists one important limitation that it cannot guarantee stability of internal dynamics at every operating point for some system parameters. A modified non-linear damping controller is proposed to improve the limitation. The proposed method has the damping term with a variable gain, thus provides improved transient performance over the whole operating range. Stability of the closed-loop system is verified by the parameter-dependent Lyapunov function. Owing to the damping term, the exact input-output linearisation is not performed; thus the output is not decoupled from internal dynamics and oscillatory transient response appears. Using the parameter-dependent Lyapunov function, it is also shown that the oscillatory output response is bounded. Improved transient performance in time-domain is validated by simulations with the topological model.

Set-point invariant control design by integrator backstepping

Invariant feedback design for nonlinear systems in state representation with Lie symmetries is considered. Existing results regarding invariant control design based on (differential) invariants of the admitted symmetry group via exact input-output linearization are extended to the backstepping algorithm for systems in feedback form. Based on invariant errors obtained by normalization an approach for the design of set-point invariant feedback is proposed. Its application is demonstrated using the control of a predator-prey bioreactor as an example.

Coordinated control of multiple HVDC links using input–output exact linearization

This paper is concerned with the investigation of a new control technique for the conventional High Voltage Direct Current (HVDC) link. The proposed technique relies upon nonlinear state feedback linearization of the AC/DC power system. The idea in input–output exact feedback linearization is to algebraically transform nonlinear systems dynamics into a linear control problem using a nonlinear pre-feedback loop, and then for the linearized power system one can design another feedback loop using a well established technique such as a linear-quadratic regulator. The primary goal of the controller presented in this paper is to contribute to the enhancement of both the transient and the small-signal stability of the power system. Since the proposed state feedback linearization does not rely on the assumption that there is only small deviation of the states from an equilibrium, the enhancement of both is feasible. The simulation results obtained in the framework of the study show that the proposed controller is capable of stabilizing the system in various system operating conditions.

Visual control through the trifocal tensor for nonholonomic robots

We present a new vision-based control approach which drives autonomously a nonholonomic vehicle to a target location. The vision system is a camera fixed on the vehicle and the target location is defined by an image taken previously in that location. The control scheme is based on the trifocal tensor model, which is computed from feature correspondences in calibrated retina across three views: initial, current and target images. The contribution is a trifocal-based control law defined by an exact input–output linearization of the trifocal tensor model. The desired evolution of the system towards the target is directly defined in terms of the trifocal tensor elements by means of sinusoidal functions without needing metric or additional information from the environment. The trifocal tensor presents important advantages for visual control purposes, because it is more robust than two-view geometry as it includes the information of a third view and, contrary to the epipolar geometry, short baseline is not a problem. Simulations show the performance of the approach, which has been tested with image noise and calibration errors.

Observer-based feedback linearization of dynamic loudspeakers with Ac amplifiers

For a reduction of nonlinear distortion produced by a dynamic loudspeaker, there exists a variety of approaches, one of them using the known principle of exact input-output linearization. In combination with a discrete state-space observer, this approach can successfully be applied as long as the amplifier driving the loudspeaker is dc-coupled. This paper discusses how ac amplifiers can be used in this context. It will be shown that an exact linearization is in general not possible with ac amplifiers due to insufficient stability of the feedback system. Two approaches will be presented that abandon the pursuit of an exact linearization in favor of stability and yield satisfactory results when implemented on a floating-point digital signal processor.

COMPENSATION OF TIME-VARYING HARMONIC DISTURBANCES ON NONLINEAR BEARINGLESS SLICE MOTORS

The rotor position of magnetic bearings or bearingless slice motors is usually subject to several harmonic disturbances with time-varying frequencies. To achieve low power consumption and good vibration suppression, efficient control algorithms have to be invoked. In this contribution, exact input-output linearization is applied to a nonlinear bearing model, followed by output regulation via the internal model principle. The resulting disturbance rejection approach does not need to know the disturbance amplitude and phase, and changes its behavior according to the measured disturbance frequency. The method is tested in simulations related to a prototype magnetic bearing.

Input–output pseudolinearization on controlled invariant submanifolds

The original notion of input–output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems. Input–output pseudolinearizing feedback laws render the input–output behavior of linearizations about nominal trajectories in the submanifold trajectory-independent and equal to that of a fixed linear time-invariant system, thereby facilitating the subsequent construction of control laws for stabilization and tracking. Sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input–output decoupling that have come to be associated with exact input–output linearization.

Assisted Guidance for a tractor-trailer with off axle hitching

A computer assisted guidance system for a tractor trailer is developed. From a practical point of view, the ideais to provide a tractor trailer operator with a mean to simplify execution of parking manoeuvres. From a theoretical point of view, we aim at providing experimental evidence of the validity of recent input-output exact linearization approaches to articulated vehicles control. These objectives are pursued by designing the guidance system, by implementing an instrumented test bench to evaluate it, and by carrying out appropriate experimental tests.

Input‐output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability

AbstractThis paper investigates the issue of the internal stability of nonlinear delay systems controlled with a feedback law that performs exact input–output, linearization and delay cancellation. In previous works the authors showed that, unlike with the case of systems without state delays, when the relative degree is equal to the number of state variables and the output is forced to be identically zero, delay systems still possess a non‐trivial internal state dynamics. Not only, in the same conditions delay systems are also characterized by a non‐trivial input dynamics. Obviously, both internal state and input dynamics should give bounded trajectories, otherwise the exact input–output linearization and delay cancellation technique cannot be applied. This paper studies the relationships between the internal state and input dynamics of a controlled nonlinear delay system. An interesting result is that a suitable stability assumption on the internal state dynamics ensures that, when the output is asymptotically driven to zero, both the state and control variables asymptotically decay to zero. Copyright © 2003 John Wiley & Sons, Ltd.