Showing papers on "Feedback linearization published in 2005"

Velocity and position control of a wheeled inverted pendulum by partial feedback linearization

Abstract: In this paper, the dynamic model of a wheeled inverted pendulum (eg, Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations This model is compared with the previous models derived for similar systems The strong accessibility condition is checked and the maximum relative degree of the system is found Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated The resulting equations are then used to design two novel controllers The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range The second controller is also a two-level controller which stabilizes the vehicle's position to the desired point, while again keeping the pitch bounded between specified limits Simulation results are provided to show the efficacy of the controllers using realistic data

A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems

Abstract: In this paper, a novel systematic design method, namely homogeneous domination approach, is developed for the global output feedback stabilization of nonlinear systems. The nonlinearities of the systems considered in this paper are neither linearly growing nor Lipschitz in immeasurable states, which make the most of existing methods inapplicable to solve the problem. By utilizing the homogeneous domination approach, a global output feedback stabilizer is explicitly constructed in two steps: i) we first design for the nominal linear system a unique homogeneous output feedback controller whose construction is genuinely nonlinear, rather than linear as used in the literature; ii) then we scale the homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally asymptotically stable. The homogeneous domination approach not only enables us to completely remove the linear growth condition, which has been the common assumption for global output feedback stabilization, but also provides us a new perspective to deal with the output feedback control problem for nonlinear systems.

Adaptive fuzzy H/sub /spl infin// stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach

Abstract: A novel adaptive fuzzy controller with H/sub /spl infin// performance is proposed for a wide class of strict-feedback canonical nonlinear systems. The systems may possess a class of uncertainties referred to as unstructured uncertain functions, which are not linearly parameterized and have no prior knowledge of the bound. The Takagi-Sugeno-type fuzzy logic systems are used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive fuzzy control with H/sub /spl infin// performance, which combines the backstepping technique and generalized small gain approach. The method preserves the three advantages, those are, the semiglobal uniform ultimate bound of adaptive control in the presence of unstructured uncertainties can be guaranteed, the adaptive mechanism with only one learning parameter is obtained and the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.

Global finite-time stabilization by output feedback for planar systems without observable linearization

Abstract: This note considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. A sufficient condition for the solvability of the problem is established. By developing a nonsmooth observer and modifying the adding a power integrator technique, we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time. As a direct application of the main result, global output feedback finite-time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous.

Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization

Abstract: This paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable/unobservable linearization. To achieve global robust stabilization via smooth output feedback, we introduce a rescaling transformation with an appropriate dilation, which turns out to be very effective in dealing with uncertainty of the system. Using this rescaling technique combined with the nonseparation principle based design method, we develop a robust output feedback control scheme for uncertain nonlinear systems in the p-normal form, under a homogeneous growth condition. The construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself. The robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict-triangular structure. Examples are provided to illustrate the results of the paper.

Robust feedback linearization and GH/sub /spl infin// controller for a quadrotor unmanned aerial vehicle

Abstract: In this paper, a mixed robust feedback linearization with linear GH controller is applied to a non linear quadrotor unmanned aerial vehicle. An actuator saturation and constrain on state space output are introduced to analyse the worst case of control law design. The results show that the overall system becomes robust when weighting functions are chosen judiciously. Performance issues of the controller are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances as well as measurement noise.

A study of brushless doubly-fed (induction) machines : contributions in machine analysis, design and control

Abstract: The Brushless Doubly-Fed Machine (BDFM) shows commercial promise as a variable speed drive or generator. However, for this promise to be realised the design of the machine must be improved beyond that proposed to date. This dissertation contributes towards this goal through machine analysis, design and control. A generalised framework is developed for a coherent and rigorous derivation of models for a wide class of BDFMs, of which machines with 'nested-loop' design rotors are a subset. This framework is used to derive coupled circuit, d-q axis, sequence components and then equivalent circuit models for the class of machines. Proofs are given for all derivations, exploiting the circulant properties of the mutual inductance matrices. The coherence between the different models allows parameters calculated for the coupled circuit model to provide parameter values for the other models. A method of model order reduction is proposed for the class ofBDFMs with 'nested-loop' rotors, and examples given of the efficacy of the procedure. The reduction method allows parameter values to be computed for a simple equivalent circuit representation of the machine. These calculated parameter values, and those for other BDFM rotor designs are verified by experimental tests on a prototype BDFM. The significance of particular equivalent circuit parameters is investigated from the model. Series rotor inductance terms are found to have a significant and direct effect on machine petformance. These terms are shown to relate directly to the design of the rotor, and are quantified using the previously developed framework. Seven different rotor designs, including a new BDFM rotor design, are considered to show how the values of these parameters change. An experimental method of parameter estimation is developed for the equivalent circuit model, and the relationship between these parameters and the parameters in other forms of the model derived. The experimental method is shown to be applicable both to standard induction machines and to BDFM machines, yielding accurate results in each case. A synchronous reference frame model for the class ofBDFMs is derived and is used to analyse the stability of the machine via a linearized model. Practical methods for the design of PID controllers are proposed to stabilise the machine using voltage source inverters. Results are presented from experimental implementations which show a significant improvement in petformance over previously published results. The non-linear control technique, feedback linearization, is applied to the BDFM and shown to have some robustness to modelling enors, in a realistic simulation. An initial attempt at implementation of the scheme is reported. Preliminary results are encouraging, and warrant further investigation. Keywords: ac machines, BDFM, Brushless Doubly Fed Machines, control, coupled circuits, dq axis, equivalent circuits, feedback linearization, model reduction, parameter estimation, synchronous reference frame

Global exponential stabilization of a class of nonlinear systems by output feedback

Abstract: This work extends the existing output feedback stabilization schemes for the systems in a "perturbed chain-of-integrator" form. In particular, we further relax the triangular-type conditions imposed on the perturbed terms and analyze the robust property of the linear output feedback control law using the newly proposed condition.

Robust feedback linearization and gh∞ controller for a quadrotor unmanned aerial vehicle

Abstract: In this paper, a mixed robust feedback linearization with linear GH1 controller is applied to a nonlinear quadrotor unmanned aerial vehicle. An actuator saturation and constrain on state space output are introduced to analyse the worst case of control law design.The results show that the overall system becomes robust when weighting functions are chosen judiciously. Performance issues of the controller are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances as well as measurement noise. K e y w o r d s: UAV, GH, sensitivity, robust linearization

A reference governor-based controller for a cable robot under input constraints

Abstract: Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots lot more challenging than their counter- part parallel actuated robots. In this brief, we look into the control design for a nonredundant cable-suspended robot under positive input constraints. The design is based on feedback linearization controllers augmented with a reference governor (RG). This RG operates in accordance with the receding horizon strategy, by generating admissible reference signals, that do not violate the input constraints. An important issue in implementing such an algorithm for nonlinear systems is to predict the system behavior in a computationally efficient way. We show that feedback lin- earization controllers with the RG can offer an efficient way to predict the system's future states, using the error dynamics of inner feedback loop. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and laboratory experiments on a 6-degree-of-freedom cable suspended robot.

Lyapunov-Based Controller for the Inverted Pendulum Cart System

Abstract: A nonlinear control force is presented to stabilize the under-actuated inverted pendulum mounted on a cart. The control strategy is based on partial feedback linearization, in a first stage, to linearize only the actuated coordinate of the inverted pendulum, and then, a suitable Lyapunov function is formed to obtain a stabilizing feedback controller. The obtained closed-loop system is locally asymptotically stable around its unstable equilibrium point. Additionally, it has a very large attraction domain.

Approximate Feedback Linearization of an Air-Breathing Hypersonic Vehicle (PREPRINT)

Abstract: : This paper describes the design of a nonlinear control law for an air-breathing hypersonic vehicle. The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics. To overcome the analytical intractability of this model, a nominal control-oriented model is constructed for the purpose of feedback control design. Analysis performed on the nominal model reveals the presence of unstable zero dynamics with respect to the output to be controlled, namely altitude and velocity. By neglecting certain weaker couplings and resorting to dynamic extension at the input side, a simplified nominal model with full vector relative degree with respect to the regulated output is obtained. Standard dynamic inversion can then be applied to the simplified nominal model, and this results in approximate linearization of the nominal model. Finally, a robust outer loop control is designed using LQR with integral augmentation in a model reference scheme. Simulation results are provided to demonstrate that the approximate feedback linearization approach achieves excellent tracking performance on the truth model for two choices of the system output. Finally, a brief case study is presented to qualitatively demonstrate the robustness of the design to parameter variations.

Linearization of large-signal scattering functions

Abstract: We describe a linearization of large-signal scattering functions describing weakly nonlinear device behavior. The linearization takes on a convenient form similar to scattering parameters that clearly illustrates the role of phase-conjugated mixing products in the theory. We develop rules for the evolution of the linearization with time. We illustrate the theory with transistor measurements and apply the theory to the characterization of the reflection coefficients of a microwave source in its large-signal operating state.

Missile guidance law design using adaptive cerebellar model articulation controller

Abstract: An adaptive cerebellar model articulation controller (CMAC) is proposed for command to line-of-sight (CLOS) missile guidance law design. In this design, the three-dimensional (3-D) CLOS guidance problem is formulated as a tracking problem of a time-varying nonlinear system. The adaptive CMAC control system is comprised of a CMAC and a compensation controller. The CMAC control is used to imitate a feedback linearization control law and the compensation controller is utilized to compensate the difference between the feedback linearization control law and the CMAC control. The online adaptive law is derived based on the Lyapunov stability theorem to learn the weights of receptive-field basis functions in CMAC control. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Then the adaptive CMAC control system is designed to achieve satisfactory tracking performance. Simulation results for different engagement scenarios illustrate the validity of the proposed adaptive CMAC-based guidance law.

Feedback linearization of active magnetic bearings: current-mode implementation

Abstract: Feedback linearization is a promising approach to the nonlinear control problem posed by active magnetic bearing systems. In this paper, feedback linearization is employed in combination with robust control techniques for the regulation of a single axis test rig actuated by a multiple pole magnetic bearing. To this end, a nonlinear polynomial model of the magnetic actuator was developed based on its experimental calibration. The effect of the amplifier and measurement system dynamics on the feedback linearization performance, was also examined, and compensation filters were developed. Finally, an uncertainty framework was proposed for the linearized plant, and a robust controller was designed via /spl mu/ synthesis. Experimental results demonstrate that the feedback-linearized active magnetic bearing system can achieve stability and the specified performance over the entire range of bearing clearance. The introduction of compensation filters is shown to be essential to this result.

A DSP-based implementation of a nonlinear model reference adaptive control for a three-phase three-level NPC boost rectifier prototype

Abstract: In this paper, the design and the implementation of a model reference adaptive control (MRAC) applied to a three-phase three-level neutral-point-clamped (NPC) boost rectifier are presented. This control strategy is developed with a view to regulate dc output and neutral point voltages and to reduce the influence of parameter variations while maintaining unity power factor. A nonlinear multiple-input multiple-output (MIMO) state space model of the rectifier is then developed in dq0 reference frame. The proposed controller is based on the use of a feedback linearization technique followed by a robust MRAC scheme allowing the design of a suitable controller applied to the plant. The control law is designed in Simulink/Matlab and applied to the converter via a 1920-Hz pulse width modulator both executed in real time using the DS1104 DSP of dSPACE. A 1.25 kW laboratory prototype is developed for validation. The experimental results are given for different operating conditions: nominal power operation, balanced and unbalanced dc load steps, boost inductor variation, and reactive power control. The proposed control law performs perfectly in a wide operation range giving low output voltage ripple, low line-current THD, a small overshoot and a fast settling time under system parameters variation.

Low-Thrust Variable-Specific-Impulse Transfers and Guidance to Unstable Periodic Orbits

Abstract: The use of a power-limited, variable-specific-impulse propulsion system to transfer a vehicle from the smaller primary to an arbitrary circular restricted three-body trajectory and the subsequent guidance along all phases of the complete trajectory is investigated. As a practical application, the transfer of a spacecraft with a finite-burn propulsion system from a low Earth orbit to the stable manifold associated with halo and vertical figure-eight orbits at the interior collinear libration point of the sun-Earth/moon system is considered. We find that an indirect method coupled with an adjoint control transformation yields a robust and efficient solution method to construct these transfers. State-feedback linearization for guidance along the powered arcs is able to adjust the control to cancel a range of sinusoidal perturbations. The dynamics of the spacecraft in the sun-Earth/moon system is approximated as a circular restricted three-body problem.

Nonlinear Control for Reconfiguration of Unmanned-Aerial-Vehicle Formation

Abstract: The design of a nonlinear controller to reconfigure a formation of a group of unmanned aerial vehicles (UAVs) is described. Reconfiguration of the formation might be needed to maintain the efficiency of the formation. Nonlinear six-degree-of-freedom, rigid-body, equations of motion developed in the virtual leader (VL)’s frame are used to model the UAVs in the formation. The formulation of the formation flight in VL frame enables the formationkeeping and formation reconfiguration to be treated in the same framework. The nonlinear equations of motion contain the wind effect terms and their time derivatives to represent the aerodynamic coupling involved in close formation flight. These wind terms are obtained by using an averaging technique that computes the effective induced wind components and wind gradients in the UAV’s body frame. Dynamics of the engine and the actuators are also included in the study. An algorithm that generates a safe and feasible trajectory, given the current position and the position to go to, has been developed. A combination of integral control, optimal LQR design, and nonlinear state feedback linearization is used in the design of the position-tracking controller. Simulation results demonstrate that the controller is capable of producing a smooth reconfiguration without using the information of the vortex-induced wind effects on the follower UAV.

Designing approach on trajectory-tracking control of mobile robot

Abstract: Based on differential geometry theory, applying the dynamic extension approach of relative degree, the exact feedback linearization on the kinematic error model of mobile robot is realized. The trajectory-tracking controllers are designed by pole-assignment approach. When angle speed of mobile robot is permanently nonzero, the local asymptotically stable controller is designed. When angle speed of mobile robot is not permanently nonzero, the trajectory-tracking control strategy with globally tracking bound is given. The algorithm is simple and applied easily. Simulation results show their effectiveness.

Trajectory tracking of large-displacement piezoelectric actuators using a nonlinear observer-based variable structure control

Abstract: The trajectory tracking of a large-displacement piezoelectric actuator (LDPA) using a nonlinear observer-based variable structure control (VSC) was developed. A mechanism of amplification using a double lever was first designed, fabricated, and tested. Subsequently, a nonlinear model for the LDPA was verified by sinusoidal response and system knowledge. Because not all of the states of the nonlinear model were available, a nonlinear state observer was employed to estimate the state (e.g., velocity, hysteresis, excitation force, and its derivative). For tracking the trajectory dominant by a specific frequency, the reference model with desired amplitude and phase features was designed. The proposed control scheme contained a feedback linearization with variable structure controller, a reference model to assign the desired dynamics, and a nonlinear state observer to estimate the unavailable state. The VSC included the following two parts: equivalent control and switching control. The equivalent control using the signals from observer and reference model was constructed to obtain the desired control behavior. Due to the existence of hysteresis, disturbance, and estimation error, the tracking performance was often deprived. In this situation, the switching control was employed to ameliorate the robust performance. The stability of the overall system was then verified by Lyapunov stability theory so that the ultimately bounded tracking was accomplished. Experiments of the LDPA were carried out to verify the usefulness of the proposed control.