Showing papers on "Feedback linearization published in 1997"

Linearizing control of magnetic suspension systems

Abstract: In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. One way to address this problem is through the use of nonlinear control techniques such as feedback linearization. For most common designs of magnetic suspensions the governing equations are in the so-called companion form, lending themselves to feedback linearization. A single degree of freedom magnetic suspension has been designed and constructed in order to compare the performance of linear and nonlinear digital control schemes in a well-controlled experimental environment. We demonstrate the superiority of nonlinear controllers over conventional controllers for systems with large variations in operating point via experiments on our system.

Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity

Abstract: With the increase in popularity of active materials for control actuation, renewed interest is evident in the derivation of control methodologies for aeroelastic systems. It has been known for some time that prototypical aeroelastic wing sections can exhibit a broad class of pathological response regimes when the system includes certaintypesofnonlinearities.Weinvestigatenonlinearcontrollawsforaeroelasticsystemsthatincludepolynomial structural nonlinearities and study the closed-loop stability of the system. It is shown that locally asymptotically stable(nonlinear)feedbackcontrollerscanbederivedfortheaeroelasticsystemusingpartialfeedbacklinearization techniques. In this case, the stability results are necessarily local in nature and are derived by considering stability of theassociated zero dynamics subsystem. Itis also demonstrated that globally stable (nonlinear)adaptivecontrol methods can be derived for a class of aeroelastic systems under consideration. Numerical simulations are used to provide empirical validation of some of the results.

Design and analysis of the nonlinear feedback linearizing control for an electromagnetic suspension system

Abstract: This paper presents some results on the robust stabilization of a class of feedback linearizable nonlinear single-input/single-output (SISO) systems exhibiting parametric uncertainty. We characterize a class of nonlinear systems with bounded uncertain parameters which can be transformed into a linear interval matrix robustness problem. We also present some analysis and implementation of nonlinear feedback linearizing control for an electromagnetic suspension (EMS) system. We show that the EMS system is nonlinear feedback linearizable and satisfies the proposed condition, and hence that the proposed nonlinear feedback controller for an EMS system is robust against mass parameter perturbation and force disturbance. Some tests are performed for making an experimental comparison between feedback linearizing control and classical state feedback control using linearization by small perturbation analysis.

Intelligent Control for an Acrobot

Abstract: The acrobot is an underactuated two-link planar robot that mimics the human acrobat who hangs from a bar and tries to swing up to a perfectly balanced upside-down position with his/her hands still on the bar. In this paper we develop intelligent controllers for swing-up and balancing of the acrobot. In particular, we first develop classical, fuzzy, and adaptive fuzzy controllers to balance the acrobot in its inverted unstable equilibrium region. Next, a proportional-derivative (PD) controller with inner-loop partial feedback linearization, a state-feedback, and a fuzzy controller are developed to swing up the acrobot from its stable equilibrium position to the inverted region, where we use a balancing controller to ‘catch’ and balance it. At the same time, we develop two genetic algorithms for tuning the balancing and swing-up controllers, and show how these can be used to help optimize the performance of the controllers. Overall, this paper provides (i) a case study of the development of a variety of intelligent controllers for a challenging application, (ii) a comparative analysis of intelligent vs. conventional control methods (including the linear quadratic regulator and feedback linearization) for this application, and (iii) a case study of the development of genetic algorithms for off-line computer-aided-design of both conventional and intelligent control systems.

Design and stability analysis of extremum seeking feedback for general nonlinear systems

Abstract: In this paper we provide the first proof of stability of an extremum seeking feedback scheme by employing the tools of averaging and singular perturbation analysis. Our scheme is much more general that the existing extremum control results which represent the plant as a static nonlinear map possibly cascaded with a linear dynamic block-we allow the plant to be a general nonlinear dynamic system (possibly non-affine in control and open-loop unstable) whose reference-to-output equilibrium map has a maximum, and whose equilibria are locally exponentially stabilizable.

Precision motion control of a magnetic suspension actuator using a robust nonlinear compensation scheme

Abstract: This paper presents a robust nonlinear compensation algorithm for realizing large travel in magnetic suspension systems suffering from parameter variations and external disturbance forces. A geometric feedback linearization technique that utilizes the complete nonlinear description of the electromagnetic field distribution is employed to obtain large travel. Robustness to uncertainties in the feedback linearized system is achieved through the development of a discrete-time delay-control-based compensation algorithm. In comparison to previous developments, the new scheme removes the constraints of triangularity conditions in compensation of unmatched uncertainties. The performance of this algorithm is experimentally investigated on a magnetic suspension system. In each of the experiments, the controller is designed using the approximate nonlinear model of the system, which is significantly different from the actual plant model. For a fixed set of gains, the robust nonlinear controller accurately stabilizes the system for a large range of ball positions. In trajectory tracking performance evaluation, the controller provides tracking accuracies that are of the same order of magnitude as the accuracy of the position sensor. Finally, when the suspended ball is impressed with an external disturbance force, the controller provides adequate model regulation and rejection of disturbance forces, demonstrating high stiffness control. The experimental results, therefore, verify the consistent performance of the algorithm in realizing large travel in spite of parameter variations and external disturbances.

Implementation of wind turbine controllers

Abstract: Three of the important generic implementation issues encountered when developing controllers for pitch-regulated constant-speed wind turbines are considered; namely, accommodation of the strongly nonlinear rotor aerodynamics, automatic controller start-up-shut-down and accommodation of velocity and acceleration constraints within the actuator. Both direct linearization and feedback linearization methods for accommodating the nonlinear aerodynamics are investigated and compared. A widely employed technique for accommodating the nonlinear aerodynamics, originally developed on the basis of physical insight, is rigorously derived and extended to cater for all wind turbine configurations. A rigorous stability analysis of controller start-up is presented for the first time, and novel design guidelines are proposed which can significantly reduce the power transients at controller start-up. The relation to anti-wind-up is noted and several aspects of an existing wind-turbine controller start-up strategy are obser...

Active suspension using preview information and model predictive control

Abstract: The objective of a suspension system is to maximize the passenger ride comfort and vehicle road holding quality. Passive systems present a trade-off between these objectives and the required suspension travel. An appropriate active suspension control overcomes this tradeoff and provides maximum ride comfort and road holding quality within the available suspension travel. In this paper, we show model predictive control (MPC) to be a design of choice for control of active suspension systems utilizing previewed road information. MPC design explicitly incorporates all hard constraints on state, control and output variables. It generalizes the approaches based on feedback linearization and dynamic inversion from single step control to multiple step control over a receding prediction horizon. MPC is shown to provide excellent improvements in the ride and road handling qualities of the vehicle over realistic terrain profiles. MPC works well even in the presence of noise in the previewed information. Implementation of MPC on the UCB active suspension test rig also shows the feasibility of the MPC algorithm in real-time application.

A study on position control of piezoelectric actuators

Abstract: The hysteresis characteristic of piezoelectric actuators makes precise position control very difficult. In this study a tracking control method for a piezoelectric actuator based on PID controller augmented with a feedback linearization loop based on the Maxwell slip model is presented. Further, the controller design is extended to include a repetitive controller. Experiments were performed on a piezoelectric 2-axis linear positioner for tracking sinusoidal waveforms and circles. The experimental results show that the tracking control performance is noticeably improved by augmenting the PID controller with a feedback linearization loop and repetitive controller.

On dynamic feedback linearization of four-dimensional affine control systems with two inputs

Abstract: This paper considers control affine systems in with two inputs, and gives necessary and sufficient conditions for dynamic feedback linearization of these systems with the restriction that the "linearizing outputs" must be some functions of the original state and inputs only. This also gives conditions for non-affine systems in .

Feedback linearizing control

Abstract: In this chapter, the basic theory of feedback linearization is presented and issues of particular relevance to process control applications are discussed. Two fundamental nonlinear controller design techniques — input-output linearization and state-space linearization — are discussed in detail. The theory also is presented for linear systems to facilitate understanding of the nonlinear results. Extensions are presented for disturbances and multivariable processes. Advanced topics such as dynamic feedback linearization, time delay compensation, constraint handling, robustness, and sampled-data systems are also discussed. A survey of process control strategies and applications shows that: (1) a variety of nonlinear controller design techniques are based on input-output linearization; (2) few experimental studies of these techniques have been presented; and (3) many important problems remain unsolved. To illustrate design and implementation issues, feedback linearizing controllers are developed for three representative processes: a continuous stirred tank reactor, a continuous fermentor, and a pH neutralization system. This chapter differs from existing reviews [69, 83, 90, 95, 99, 100, 126, 134] of feedback linearization by providing a balanced discussion of theoretical and practical issues of interest to process control engineers.

Nonlinear control of a permanent magnet synchronous motor with disturbance torque estimation

Abstract: This paper introduces a sensorless nonlinear control scheme for controlling the speed of a permanent magnet synchronous motor (PMSM) driving an unknown load torque. The states of the motor and disturbance torque are estimated via an extended nonlinear observer avoiding the use of mechanical sensors. The control strategy is an exact feedback linearization law, with trajectory tracking evaluated on estimated values of the PMSM states and the disturbance torque. The system performance is evaluated by simulations.

Feedback linearization and fuzzy control for conical magnetic bearings

Abstract: Conical magnetic bearings with radial and thrust (axial) control using the input-output feedback linearization method are considered. By suitable selection of nine output variables, the nonlinear magnetic bearing system is transformed to nine linear decoupled subsystems with no internal dynamics using feedback linearization control. Furthermore, a hybrid approach integrating feedback linearization and fuzzy control is proposed for improving the transient performance and robustness of the nonlinear magnetic bearings. Computer simulations are shown to illustrate the effectiveness of the proposed control strategy for simultaneous rotor-shaft speed tracking control and gap deviations regulation.

Adaptive Nonlinear Attitude Control and Momentum Management of Spacecraft

Abstract: An indirect adaptive nonlinear controller is investigated for attitude control and momentum management of evolutionary spacecraft. The control law is based on the theory of nonlinear feedback linearization. A new state transformation is introduced: one that converts the original nonlinearsystem into normal canonical form. Once in canonical form, nonlinear feedback is used to generate a linear response in the transformed coordinates. To make the nonlinear controller adaptive, a parameter identie cation scheme, utilizing an extended Kalman e lter, is added for mass property estimation. Probing signals are introduced to enhance the observability of the mass properties. Simulation results show that the adaptive nonlinear controller stabilizes the International Space Station during mass property changes, successfully performs momentum management, and provides real-time estimates of the mass properties in a realistic environment.

Nonlinear missile autopilot design using time-scale separation

Abstract: Time-Scale separation helps improve the robustness of feedback linearized autopilots by simplifying the feedback linearization maps, and by permitting the design of low-order controllers. This paper presents the development of three distinct timescale separation schemes for the design of feedback linearized missile autopilots. A six degrees-of-freedom missile model is used in this work. The performance of these autopilots are compared with the design that does not use time-scale separation. Simulation results illustrating controller tracking performance and robustness are presented.

Feedback control of affine nonlinear singular control systems

Abstract: This paper discusses feedback control problems for affine nonlinear singular systems. Namely, the problems of regularization (regular singular systems have for a particular initial state and input, a unique solution), non-interaction and exact linearization. First, an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced. This algorithm resembles the well-known constrained dynamics algorithm for affine nonlinear systems. For regularizable affine nonlinear singular systems, necessary and sufficient conditions for the solvability of the non-interacting control problem are derived. They are based on another algorithm producing a sequence of integers, the generalization of the well known notion of relative degree for usual affine nonlinear systems. Finally, the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed. An example is provided to illustrate the main results.

Quadratic forms and approximate feed back linearization in discrete time

Abstract: Quadratic feedback linearization is discussed for discrete-time systems, i.e. approximate feedback linearization up to the second order with respect to input and state variables. After introducing in discrete time two equivalence classes, invariant under quadratic static state feedback and diffeomorphism, two canonical quadratic representations are proposed. Then it is shown that any nonlinear discrete-time dynamics, which are controllable in their first approximations, can be linearized up to the second order under dynamic feedback. The results stated here can be considered as the general discrete-time analogues of the continuous-time ones (Kang and Krener 1992).

Modeling and control design for a computer-controlled brake system

Abstract: The brake subsystem is one of the most significant parts of a vehicle with respect to safety. A computer-controlled brake system has the capability of acting faster than the human driver during emergencies, and therefore has the potential of improving safety of the vehicles used in the future intelligent transportation systems (ITSs). In this paper we consider the problem of modeling and control of a computer-controlled brake system. The brake model is developed using a series of experiments conducted on a test bench which contains the full scale brake subsystem of a Lincoln town car and a computer-controlled actuator designed by Ford Motor Company. The developed model has the form of a first-order nonlinear system with the system nonlinearities lumped in the model coefficients. The unknown model parameters are identified by applying curve fitting techniques to the experimental data. The major characteristics of the system such as static friction, dead zones, and hysteresis have been identified in terms of model parameters. The brake controller design makes use of a standard feedback linearization technique along with intuitive modifications to meet the closed-loop performance specifications. The simulation results show that the proposed controller guarantees no overshoot and zero steady-state error for step inputs. Test of the same controller using the experimental bench setup demonstrates its effectiveness in meeting the performance requirements.