Nonlinear control of a flexible aeroelastic system

Although it is a common practice in the field of Dynamics to treat a system as being linear, the assumption of linearity is only valid in situations where the effect of any nonlinearities is minimal. Significant nonlinear behaviour (such as Limit Cycle Oscillations) has been observed in many practical manifestations of aeroelastic systems, highlighting the need to account for system nonlinearities. A consequence of incorporating nonlinearity into the model is that the application of linear control methods becomes inadequate when the system operates in a substantially nonlinear regime. Thus, the present work addresses both these concerns by applying nonlinear control on an aeroelastic system consisting of a flexible wing with a structural nonlinearity. The Feedback Linearisation method is employed to render the system linear, such that linear control methods are applicable. The utility of the Small Gain Theorem and Adaptive Feedback Linearisation in situations where errors in the parameters describing the nonlinearities are present is demonstrated

Feedback Linearization in Systems with Nonsmooth Nonlinearities

This paper aims to elucidate the application of feedback linearization in systems having nonsmooth nonlinearities. With the aid of analytical expressions originating from classical feedback linearization theory, it is demonstrated that for a subset of nonsmooth systems, ubiquitous in the structural dynamics and vibrations community, the theory holds soundly. Numerical simulations on a three-degree-of-freedom aeroservoelastic system are carried out to illustrate the application of feedback linearization for a specific control objective, in the presence of dead-zone and piecewise linear structural nonlinearities in the plant. An in-depth study of the arising zero dynamics, based on a combination of analytical formulations and numerical simulations, reveals that asymptotically stable equilibria exist, paving the way for the application of feedback linearization. The latter is demonstrated successfully through pole placement on the linearized system

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closedloop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems e that the input and output must share the same degrees of freedom

Feedback Linearisation for Nonlinear Vibration Problems

Feedback linearisation is a well-known technique in the controls community but has not been widely taken up in the vibrations community. It has the advantage of linearising nonlinear system models, thereby enabling the avoidance of the complicated mathematics associated with nonlinear problems. A particular and common class of problems is considered, where the nonlinearity is present in a system parameter and a formulation in terms of the usual second-order matrix differential equation is presented. The classical texts all cast the feedback linearisation problem in first-order form, requiring repeated differentiation of the output, usually presented in the Lie algebra notation. This becomes unnecessary when using second-order matrix equations of the problem class considered herein. Analysis is presented for the general multidegree of freedom system for those cases when a full set of sensors and actuators is available at every degree of freedom and when the number of sensors and actuators is fewer than the number of degrees of freedom. Adaptive feedback linearisation is used to address the problem of nonlinearity that is not known precisely. The theory is illustrated by means of a three-degree-of-freedom nonlinear aeroelastic model, with results demonstrating the effectiveness of the method in suppressing flutter

A nonlinear controller for flutter suppression: from simulation to wind tunnel testing

Active control for flutter suppression and limit cycle oscillation of a wind tunnel wing section is presented. Unsteady aerodynamics is modelled with strip theory and the incompressible two-dimensional classical theory of Theodorsen. A good correlation of the stability behaviour between simulation and experimental data is achieved. The paper focuses on the introduction of a nonlinearity in the plunge degree of freedom of an experimental wind tunnel test rig and the design of a nonlinear controller based on partial feedback linearization. To demonstrate the advantages of the nonlinear synthesis on linear conventional methods, a linear controller is implemented for the nonlinear system that exhibits limit cycle oscillations above the linear flutter speed. The controller based on partial feedback linearization outperforms the linear control strategy based on pole placement. Whereas feedback linearization allows to suppress fully the limit cycle oscillations, the pole placement fails to achieve any significant reduction in amplitude

Experimental and numerical study of nonlinear dynamic behaviour of an aerofoil

The paper describes the experimental and numerical investigations on a plunge-pitch aeroelastic system with a hardening nonlinearity. The goals of this work are to achieve a better understanding of the behaviour of the model while it undergoes Limit Cycle Oscillations and to tune the numerical model to reproduce both linear and nonlinear aeroelastic response observed in the aeroelastic system. Moreover, this work is part of an overall project, which final aims are to test various control strategies for flutter suppression on the nonlinear aeroealstic system. The experimental model consists of a rigid wing supported by adjustable vertical and torsional leaf springs provided with a trailing edge control surface. In the present work the rig is extended to include a nonlinearity introduced by connecting the plunge degree of freedom to a perpendicular pretensioned cable. The numerical model is a 2 dof reduced order model representing the dynamics properties of the real system, the nonlinearity is incorporated in the state space equations by adding the cubic and fifth order terms in the stiffness matrix; the unsteady aerodynamic is modelled with strip theory and the incompressible two-dimensional classical theory of Theodorsen. In addition to provide a comparison with the experimental results, the numerical model has been used during the course of the project as an interactive tool to guide the choice of the stiffness stetting of the system. A comparison between experimental and numerical results is provided as well; for the linear model, they show a good agreement in the linear case, albeit not so much with the damping ratios. Once the nonlinearity is added, good agreement is achieved with the plunge LCO, but there still is room for improvement with pitch LCO. An in-depth investigation will be carried out to improve model tuning with respect to all parameters of the model

Feedback Linearisation for Nonlinear Vibration Problems

Feedback linearisation is a well-known technique in the controls community but has not been widely taken up in the vibrations community. It has the advantage of linearising nonlinear system models, thereby enabling the avoidance of the complicated mathematics associated with nonlinear problems. A particular and common class of problems is considered, where the nonlinearity is present in a system parameter and a formulation in terms of the usual second-order matrix differential equation is presented. The classical texts all cast the feedback linearisation problem in first-order form, requiring repeated differentiation of the output, usually presented in the Lie algebra notation. This becomes unnecessary when using second-order matrix equations of the problem class considered herein. Analysis is presented for the general multidegree of freedom system for those cases when a full set of sensors and actuators is available at every degree of freedom and when the number of sensors and actuators is fewer than the number of degrees of freedom. Adaptive feedback linearisation is used to address the problem of nonlinearity that is not known precisely. The theory is illustrated by means of a three-degree-of-freedom nonlinear aeroelastic model, with results demonstrating the effectiveness of the method in suppressing flutter

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closedloop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems e that the input and output must share the same degrees of freedom