Showing papers on "Feedback linearization published in 1999"

Nonlinear Systems: Analysis, Stability, and Control

Abstract: 1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References.

Nonlinear Control Systems II

Abstract: From the Publisher: "This book incorporates recent advances in the design of feedback laws to the purpose of globally stabilizing nonlinear systems via state or output feedback. It is a continuation of the first volume by Alberto Isidori on Nonlinear Control Systems. Specifically this second volume will cover: Stability analysis of interconnected nonlinear systems; the notion of input-to-state stability and its role in analysing stability of cascade-connected or feedback-connected systems; the notion of dissipativity and its consequences (passivity and "gain"); robust stabilization in the case of parametric uncertainties; the case of state feedback (global or semi-global stabilization); the case of output feedback (semi-global stabilization); robust stabilization in the case of unstructured perturbations; feedback design via the small-gain approach; robust semi-global stabilization via output feedback; methods for asymptotic tracking, disturbance rejection and model following; global and semi-global analysis; normal forms for multi-input multi-output nonlinear systems form a global point of view; and their role in feedback design."--BOOK JACKET.

Trajectory tracking control of a four-wheel differentially driven mobile robot

Abstract: We consider the trajectory tracking control problem for a 4-wheel differentially driven mobile robot moving on an outdoor terrain. A dynamic model is presented accounting for the effects of wheel skidding. A model-based nonlinear controller is designed, following the dynamic feedback linearization paradigm. An operational nonholonomic constraint is added at this stage, so as to obtain a predictable behavior for the instantaneous center of rotation thus preventing excessive skidding. The controller is then robustified, using conventional linear techniques, against uncertainty in the soil parameters at the ground-wheel contact. Simulation results show the good performance in tracking spline-type trajectories on a virtual terrain with varying characteristics.

Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity

Abstract: Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.

Application of a multivariable feedback linearization scheme for rotor angle stability and voltage regulation of power systems

Abstract: This paper investigates the application of a nonlinear controller to the multi-input multi-output model of a system consisting of a hydraulic turbine and a synchronous generator. The controller proposed is based on a feedback linearization scheme. Its main goal is to control the rotor angle as well as the terminal voltage, to improve the system's stability and damping properties under large disturbances and to obtain good post-fault voltage regulation. The response of the system is simulated in the presence of a short-circuit at the terminal of the machine in two different configurations and compared to the performance of a standard IEEE type 1 voltage regulator, PSS and a PID speed regulator.

A general framework for cobot control

Abstract: A general framework is presented for the design and analysis of cobot controllers. Cobots are inherently passive robots intended for direct collaborative work with a human operator. While a human applies forces and moments, the controller guides motion by tuning the cobot's set of continuously variable transmissions. In this paper, a path following controller is developed that steers the cobot so as to asymptotically approach and follow a pre-planned path. The controller is based on feedback linearization. Generality across cobot architectures is assured by designing the controller in task space and developing transformations between each of four spaces: task space, joint space, a set of coupling spaces, and steering space.

Efficiency-optimized direct torque control of synchronous reluctance motor using feedback linearization

Abstract: In this paper, a nonlinear controller capable of high dynamic torque regulation and efficiency optimization of the synchronous reluctance motor (SynRM) using input-output feedback linearization is proposed. The cross-coupling effects in the SynRM model and the torque nonlinearity due to the iron losses in torque-speed characteristics of the SynRM are discussed. The criterion for the efficiency optimization is also introduced and investigated. Since the proposed nonlinear controller directly regulates the torque by selecting the product of d- and q-axes torque currents as one of the output variables, the nonlinear and cross-coupling aspects between the d-and q-axes torque currents and the terminal currents can he eliminated. Hence, the linear torque-speed characteristic can be achieved. In addition, by controlling the power loss-minimizing criterion directly, the proposed controller can optimize the efficiency of the SynRM without deteriorating the dynamics performance.

Tutorial on nonlinear backstepping: Applications to ship control

Abstract: The theoretical foundation of nonlinear backstepping designs is presented in a tutorial setting. This includes a brief review of integral backstepping, extensions to SISO and MIMO systems in strict feedback form and physical motivated case studies. Parallels and differences to feedback linearization where it is shown how so-called good nonlinearities can be exploited in the design are also made. Nonlinear, optimal and robust backstepping are discussed in a separate section where parallels to linear quadratic optimal control and H∞-control are drawn. In addition, inverse optimality is discussed as a nonlinear design tool. Physics is put into control by using mechanical systems like mass-damper-springs and ship models in the case studies. Lyapunov theory is used to prove convergence and stability for all control laws where energy dissipation is obtained by exploiting physical model properties.

A model predictive control-based approach for spacecraft formation keeping and attitude control

Abstract: In this paper we report on the application of a model predictive control-based approach to the design of a controller for formation keeping and formation attitude control, with applications to spacecraft formation flight problems such as NASA's DS3 mission. Control laws for formation keeping and attitude control are designed using a combined approach of feedback linearization and model predictive control. Actuator saturation is incorporated into the controller design. Switching between coordinated frames is incorporated to overcome singularities associated with local feedback linearization.

Sensitivity of Trajectory Prediction in Air Traffic Management

Abstract: Trajectory prediction in air trafe c management computes the most likely or the most desirable aircraft trajectories by using models of aircraft performance and atmospheric conditions, as well as measurements of aircraft states. In comparison, actual trajectories are obtained using feedback control from a pilot or autopilot to track e ight objectives, while theaircrafte iesthrough an actual atmosphere. This paperintroduces the concept ofclosedloop sensitivities, which are dee ned as differences between actual and computed trajectories per unit of modeling errors, in thepresenceof pilot/autopilotfeedback controls.Modeling errorsareexpressed asuncertain parameters and/or uncertain functions. Pilot/autopilot control actions are approximated by nonlinear feedback control laws, designedwith themethod of feedback linearization. Both theaircraft equations of motion and the feedbackcontrol laws are linearized around computed reference trajectories, and these linearized equations are used to determine expressions for closed-loop terminal sensitivities. The proposed method is applied to the Center/Terminal Radar Approach Control (TRACON) Automation System as well as e ight management systems.

Fuzzy local linearization and local basis function expansion in nonlinear system modeling

Abstract: Fuzzy local linearization is compared with local basis function expansion for modeling unknown nonlinear processes. First-order Takagi-Sugeno fuzzy model and the analysis of variance (ANOVA) decomposition are combined for the fuzzy local linearization of nonlinear systems, in which B-splines are used as membership functions of the fuzzy sets for input space partition. A modified algorithm for adaptive spline modeling of observation data (MASMOD) is developed for determining the number of necessary B-splines and their knot positions to achieve parsimonious models. This paper illustrates that fuzzy local linearization models have several advantages over local basis function expansion based models in nonlinear system modeling.

A power-factor controller for single-phase PWM rectifiers

Abstract: A novel power-factor controller for single-phase pulsewidth modulated rectifiers is proposed. The unity power-factor controller for a sinusoidal input current is derived using the feedback linearization concept. Two active switches and two diodes are utilized for AC-to-DC power conversion. Experimental results obtained on a 4 kW prototype are discussed.

Analytical analysis and feedback linearization tracking control of the general Takagi-Sugeno fuzzy dynamic systems

Abstract: The Takagi-Sugeno (TS) fuzzy modeling technique, a black-box discrete-time approach for system identification, has widely been used to model behaviors of complex dynamic systems. The analytical structure of TS fuzzy models, however, is unknown, causing at two major problems. First, the fuzzy models cannot be utilized to design controllers of the physical systems modeled. Second, there is no systematic technique for designing a controller that is capable of controlling any given TS fuzzy model to achieve the desired tracking or setpoint control performance. In this paper, we provide solutions to these problems. We have proved that a general class of TS fuzzy models is a nonlinear time-varying ARX (Auto-Regressive with eXtra input) model. We have established a simple condition for analytically determining the local stability of the general TS fuzzy dynamic model. The condition can also be used to analytically check the quality of a TS fuzzy model and invalidate the model if the condition warrants. We have developed a feedback linearization technique for systematically designing an output tracking controller so that the output of a controlled TS fuzzy system of the general class achieves perfect tracking of any bounded time-varying trajectory. We have investigated the stability of the tracking controller and established a condition, in relation to the stability of non-minimum phase systems, for analytically deciding whether a stable tracking controller can be designed using our method for any given TS fuzzy system. Three numerical examples are provided to illustrate the effectiveness and utility of our results and techniques.

Switched nonlinear control of a VSTOL aircraft

Abstract: A longitudinal model of a vectored-thrust Vertical and/or Short Take-Off and Landing (VSTOL) aircraft, which operates in three distinct modes, is a high-dimensional system whose performance can be enhanced with the use of switched nonlinear control. The aircraft's performance is limited by physical constraints on such parameters as ground speed, angle of attack, and thrust, which are summarized by the aerodynamic flight envelope. We specify a least-restrictive control law which will keep the aircraft within this envelope. We independently examine the aerodynamic flight envelope constraints and design the nonlinear controller for each mode using approximate feedback linearization, then combine the results to guarantee tracking within a "safe" envelope. We provide an example of switching between these modes in a short take-off maneuver based on pilot data.

Local asymptotic stability for nonlinear state feedback delay systems

Abstract: In previous papers the authors presented an elementary theory for feedback control of nonlinear delay systems, in which methods of standard nonlinear analysis were used to solve control problems such as output regulation and tracking, disturbance decoupling and model matching for a class of nonlinear delay systems. Output control was obtained by means of state feedback control laws, but nothing was said about the behavior of the system state. In this paper some results have been obtained about this problem. It is proved that if the output and its derivatives up to a given order are driven to zero, and if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, and the initial state is inside such neighborhood, then the system state asymptotically goes to zero. Simulations on nonlinear delay systems unstable in open loop match the theoretical results.

Feedback linearization design of a ship steering autopilot with saturating and slew rate limiting actuator

Abstract: A full non-linear model including sea-state modelling is used in the design for a ship steering autopilot. This has been done before. However, rather than a conservative design to avoid amplitude and slew rate limit in the rudder, we show how these limits can be accommodated without otherwise compromising the performance. Thus, saturation and slew rate limiting are accepted as inevitable consequence of high performance rather than something to be avoided at all cost. Copyright © 1999 John Wiley & Sons, Ltd.

A new sliding mode position controller with adaptive load torque estimator for an induction motor

Abstract: A new sliding mode control algorithm with an adaptive load torque estimator is presented to control the position of the induction motor in this paper. First, the rotor flux is estimated with the simplified rotor flux observer in the rotor reference frame and the feedback linearization theory is used to decouple the rotor position and the rotor flux amplitude. Then, a new sliding mode position controller with an adaptive load torque estimator is designed to control the position of the induction motor such that the chattering effects associated with the classical sliding mode position controller can be eliminated. Stability analysis is carried out using the Lyapunov stability theorem. Experimental results are presented to confirm the characteristics of the proposed approach. The good position tracking and load regulating responses can be obtained by the proposed position controller.

Simultaneous Stabilization of Linear and Nonlinear Systems by Means of Nonlinear State Feedback

Abstract: The simultaneous stabilization (resp., asymptotic stabilization) of a countable family of control systems consists of finding a control which stabilizes (resp., asymptotically stabilizes) all the systems in the family. In this paper, we introduce a new method which enables us to show that, given any countable family of stabilizable nonlinear systems, there exists a continuous state feedback law which simultaneously stabilizes (not asymptotically) the family. Then, by enriching this method, we prove that any finite family of stabilizable linear time invariant (LTI) systems can be simultaneously exponentially stabilized by means of nonlinear time-varying state feedback. We also derive sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of LTI systems. Finally, sufficient conditions for the simultaneous asymptotic stabilizability of finite families of nonlinear systems are provided and used for the simultaneous asymptotic stabilization of certain pairs of nonlinear homogeneous systems.

On the recoverability of nonlinear state feedback laws by extended linearization control techniques

Abstract: Extended linearization is the process of factoring a nonlinear system into a linear-like structure x/spl dot/=A(x)x+ B(x)u which contains state-dependent coefficient (SDC) matrices. An extended linearization control technique is a technique which: 1) treats the SDC matrices A(x) and B(x) as being constant, and 2) uses a linear control synthesis method on the linear-like structure to produce a closed-loop SDC matrix which is pointwise Hurwitz. This paper investigates the recoverability of nonlinear state feedback laws using extended linearization control techniques with particular focus on the state-dependent Riccati equation method. An example is presented where it is attempted to recover an optimal feedback law. It is shown that there exists no extended linearization control technique that is capable of recovering the given law. It is then shown how the feedback law can be recovered by using: a state-dependent state weighting matrix and a nonsymmetric solution of the state-dependent Riccati equation which simultaneously satisfies a symmetry condition.

Precision robotic control of agricultural vehicles on realistic farm trajectories

Abstract: High-precision “autofarming”, or precise agricultural vehicle guidance, is rapidly becoming a reality thanks to increasing computing power and carrier-phase differential GPS (“CPDGPS”) position and attitude sensors. Realistic farm trajectories will include not only rows but also arcs created by smoothly joining rows or path-planning algorithms, spirals for farming center-pivot irrigated fields, and curved trajectories dictated by nonlinear field boundaries. In addition, fields are often sloped, and accurate control may be required either on linear trajectories or on curved contours. A three-dimensional vehicle model which adapts to changing vehicle and ground conditions was created, and a low-order model for controller synthesis was extracted based on nominal conditions. The model was extended to include a towed implement. Experimentation showed that an extended Kalman filter could identify the vehicle's state in real-time. An approximation was derived for the additional positional uncertainty introduced by the noisy “lever-arm correction” necessary to translate the GPS position measurement at the roof antenna to the vehicle's control point on the ground; this approximation was then used to support the assertion that attitude measurement accuracy was as important to control point position measurement as the original position measurement accuracy at the GPS antenna. The low-order vehicle control model was transformed to polar coordinates for control on arcs and spirals. Experimental data showed that the tractor's control, point tracked an arc to within a −0.3 cm mean and a 3.4 cm standard deviation and a spiral to within a −0.2 cm mean and a 5.3 cm standard deviation. Cubic splines were used to describe curve trajectories, and a general expression for the time-rate-of-change of curve-related parameters was derived. Four vehicle control algorithms were derived for curve tracking: linear local-error control based on linearizing the vehicle about the curve's radius of curvature, linear finite-preview control using discrete linear quadratic tracking, nonlinear local error control based on feedback linearization, and nonlinear finite-preview control using nonlinear optimization techniques. The first three algorithms experimentally demonstrated mean tracking errors between zero and four centimeters and standard deviations of roughly four to ten centimeters. The fourth algorithm was computationally too expensive to implement with current technology. In experiment, the feedback linearization algorithm outperformed the other two control algorithms and also used the most control effort. For control on sloped terrain, a variation on bias estimation (termed slope-adjusted bias estimation) was created, based on the terrain slope information calculated from vehicle attitude measurements. Slope-adjusted bias estimation demonstrated a 25% improvement in the standard deviation of the tractor's row-tracking error over “normal” bias estimation on terrain sloped at grades up to 28%. The CPDGPS attitude information was also used to develop a contour-tracking controller that tracked a contour to within a mean height error of 0.5 cm and a standard deviation of 4.3 cm without any prior knowledge of the terrain. These real-time vehicle control results, applicable to any front-wheel-steered vehicle, demonstrate that accurate real-time control is possible over a variety of trajectories needed in a commercial autofarming system. This research is a significant step towards completely automating tractor control because farmers can now build global trajectories composed of the different types of trajectory “building blocks” developed here. Experimental results demonstrate that farmers can expect precision tracking down to the limit of the GPS position and attitude sensors.

Global output-feedback tracking for a benchmark nonlinear system

Abstract: The output-feedback global tracking problem is solved for the well-known nonlinear benchmark RTAC (rotational-translational actuator) system, where one of the unmeasured states appears quadratically in the state equations. Our observer-controller backstepping design yields a nonlinear output-feedback controller that forces the translational displacement to globally asymptotically track an appropriate time-varying signal. The proposed solution is new even for the case of global output-feedback stabilization, namely when the reference signal is zero.

Tracking Control of Robot Manipulator Using Sliding Mode Controller With Performance Robustness

Abstract: The tracking control problem of robot manipulator is considered in this paper. A sliding mode controller design with global invariance is proposed using the concept of extended system and feedback linearization. The sliding surface is assigned such that the sliding mode motion will occur while the proposed control law is applied. This results in a system with global invariance. The stability and performance of the resulting system can be guaranteed by the proposed systematic design procedure.