Shakir Jiffri

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 amplitudes

Experimental Nonlinear Control for Flutter Suppression in a Nonlinear Aeroelastic System

Experimental implementation of input–output feedback linearization in controlling the dynamics of a nonlinear pitch–plunge aeroelastic system is presented. The control objective is to linearize the system dynamics and assign the poles of the pitch mode of the resulting linear system. The implementation 1) addresses experimentally the general case where feedback linearization-based control is applied using as the output a degree of freedom other than that where the physical nonlinearity is located, using a single trailing-edge control surface, to stabilize the entire system; 2) includes the unsteady effects of the airfoil’s aerodynamic behavior; 3) includes the embedding of a tuned numerical model of the aeroelastic system into the control scheme in real time; and 4) uses pole placement as the linear control objective, providing the user with flexibility in determining the nature of the controlled response. When implemented experimentally, the controller is capable of not only delaying the onset of limit-cycle oscillation but also successfully eliminating a previously established limit-cycle oscillation. The assignment of higher levels of damping results in notable reductions in limit-cycle oscillation decay times in the closed-loop response, indicating good controllability of the aeroelastic system and effectiveness of the pole-placement objective. The closed-loop response is further improved by incorporating adaptation so that assumed system parameters are updated with time. The use of an optimum adaptation parameter results in reduced response decay times.

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.

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.

Adaptive Feedback Linearisation and Control of a Flexible Aircraft Wing

Active control systems are used on aircraft to reduce loads due to gusts and manoeuvres, reduce the effect of noise, and could also increase the speed at which flutter occurs. Unfortunately most aeroservoelastic systems include some form of nonlinearity, and this increases the complexity of the feedback system and also facilitates the likelihood of Limit Cycle Oscillations occurring. Previous work on the application of Adaptive Feedback Linearisation to aeroelastic systems has demonstrated the promising potential of this method when applying control in the presence of substantial nonlinearity. In this work, Adaptive Feedback Linearisation is applied to an aeroelastic model of a cantilevered flexible wing with a cubic hardening structural nonlinearity in an engine pylon. Using assumed vibration modes, a suitable model of the wing is developed, into which structural nonlinearity is incorporated. Closed-loop control is implemented on the aeroservoelastic system via linearising feedback computed through the Adaptive Feedback Linearisation algorithm. The advantage of the latter is the guaranteed stability of the closed-loop aeroelastic system, despite lack of knowledge of the exact description of the nonlinearity. It is shown how such an approach can be used to delay the onset of flutter or limit cycle oscillations.

Nonlinear Control of an Aeroelastic System with a Non-smooth Structural Nonlinearity

Non-smooth nonlinearities such as freeplay, bilinear/piece-wise linear stiffness are among the various types of nonlinearity that have been encountered in aeroelastic systems. Freeplay, for example, may begin to appear as a result of ageing of components such as bolted joints and control surfaces, and has been known to be the cause of flutter-induced limit cycle oscillation (LCO). Therefore, it is evident that effectively controlling these nonlinearities is essential in avoiding the onset of LCO, or indeed any other type of nonlinear response. The present paper addresses the control of systems with non-smooth structural nonlinearities, through application of the feedback linearisation method. In systems with smooth nonlinearities, the required nonlinear feedback is also smooth, and therefore does not give rise to complexities associated with the feedback linearisation method. On the other hand, when controlling systems with non-smooth nonlinearities, the necessary control inputs are also non-smooth, and the applicability of feedback linearisation to such systems is of interest. This task is undertaken in the present work, through the use of numerical simulations on a 3 degree of freedom aeroservoelastic model. An example of a case where the parameterisation of the nonlinearity is uncertain is also addressed.

Experimental feedback linearisation of a non-smooth nonlinear system by the method of receptances.

Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour.

Enriching balancing information using the unbalance covariance matrix

Abstract Traditionally, rotor balancing is performed based only on vibration readings from either a balancing machine or from a machine in which the rotor is being balanced in-situ. These readings cannot reflect the complete state of unbalance in the rotor. The reason for this is that higher frequency modes do not make a significant contribution to response in any one operating condition. The resolution of measuring instrumentation is always limited and, as demands grow for ever-improved balance quality, this instrumentation struggles more and more with reducing signal-to-noise ratios. When balance corrections are made to a rotor based only on these vibration readings, the components of unbalance that tend to excite only the higher modes of the original configuration can make a significant contribution to response if the properties of the stator change. This article presents a novel approach to robust balancing. It relies on the use of additional information in the form of a rotor unbalance covariance matrix. In theory, this covariance matrix could be obtained if a large sample from the population of all rotors of this type could be tested in a very high-quality (and high-speed) balancing machine. This suggestion is impracticable in all real situations. However, it is entirely conceivable that modelling of the manufacturing processes used to create the rotor could deliver this covariance matrix. This article begins by illustrating how such a covariance matrix might be obtained from modelling and then goes on to explain how the information within the covariance matrix can be combined with a set of measurements from a specific rotor to provide an improved estimate of the actual state of unbalance on that rotor. Examples are included to demonstrate the proposed robust balancing method.