Open-loop Frequency Response Function Research Articles

Effect of a fluid layer on the sound radiation of a plate and its active control

In this paper, a baffled plate facing a layer of fluid is used to investigate the effects of the radiating environment on the plate׳s sound radiation and its active control. By varying the thickness of the fluid layer, different radiation environments are presented to the plate, resulting in a variation in the efficiencies and shapes of the radiation modes of the plate. As the design of feed-forward control of the radiated sound power and of feedback control of the vibration velocity or volume velocity is limited by the properties of the secondary control path (an open-loop frequency response function), the performance of the control system may be deteriorated if a controller optimally designed for one radiation environment is used for a different environment. The effects of radiation environment on the properties of the secondary control path and performance of active control are investigated.

Comparison of decentralized velocity feedback control for thin homogeneous and stiff sandwich panels using electrodynamic proof-mass actuators

Theoretical and experimental work is presented to compare the effect of decentralised velocity feedback control on thin homogeneous and sandwich panels. The decentralised control system consists of five control units, which are composed of a proof-mass electrodynamic actuator with an accelerometer underneath its footprint and an analogue controller. The stability of the feedback loops is analysed by considering the sensor-actuator open-loop frequency response function of each control unit and the eigenvalues of the fully populated matrix of open-loop frequency response functions between the five sensors and five actuators. The control performance is then analysed in terms of the time-averaged total kinetic energy and total sound power radiated by the two panels. The results show that for a stiff sandwich panel higher stable feedback gains can be implemented than on a thin homogeneous panel of comparable weight per unit area. Moreover the implementation of decentralised velocity feedback can offset some of the undesirable sound transmission properties of lightweight sandwich structures by efficiently reducing structural vibration and sound power radiation in the mid audio frequency range.

A smart panel with active damping wedges along the perimeter

This paper discusses the practical implementation of decentralized velocity feedback on athin rectangular panel using sixteen triangularly shaped piezoceramic patch actuators withthe base edges uniformly distributed along the perimeter of the panel and accelerometersensors located at the tips of the actuators. In the first part of the paper, thesensor–actuator open loop frequency response function of one feedback loop is modelledand analysed in order to study the principal stability properties of a single control unit. Inparticular an elemental model is developed for studying the bending excitation and passivestiffness and inertia effects produced by the triangular piezoceramic actuator and forinvestigating the resilient effect of the clamping frame that holds the panel. Thesimulated frequency response function is validated experimentally and contrasted withthat obtained from a conventional model of the bending excitation produced bytriangularly shaped distributed transducers. In the second part of the paper,the stability and control performance of sixteen decentralized feedback loops areinvestigated experimentally. Six rectangular panels have been built and equipped withaccelerometer sensors and piezoceramic triangular actuators of various geometriessuch that the effects of the base width, height and base area can be examined.

Direct Optimal Controller Identification for Uncertain Systems using Frequency Response Function Data

Here we present a new approach to optimal controller identification which unifies system identification and optimal control theory. Starting with empirical, open-loop frequency response function (FRF) data from a system, it is shown that the optimal controller can be identified directly without performing the intermediary steps of system identification and controller design. The primary benefit is that we are able to work directly with the measured data and the uncertainties inherent in it. Further, we go on to show a method of incorporating the empirical FRF uncertainty into the cost for robustness against plant uncertainty. This method leads to a more precise identification of H2 and LQG controllers since it avoids the residual errors associated with performing the traditional intermediary step of system identification, while concurrently accounting for measured system uncertainty.

Modelling of a piezoceramic patch actuator for velocity feedback control

This paper discusses the modelling of a thin panel with a velocity feedback controlunit, which is formed by a piezoceramic patch actuator and, at its centre, anideal point velocity sensor. The model has been used to predict the open loopsensor–actuator frequency response function in a wide frequency band, up to 80 kHz, sothat the stability of the feedback control loop can be properly assessed usingthe Nyquist criterion. In particular the inertia and stiffness effects produced bythe actuator on the frequency response function have been analysed. Simulationresults have highlighted that the inertia effect produces amplitude reduction andphase lag at higher frequencies. The stiffness effect reduces the amplitude at lowfrequencies, decreases the phase lag at higher frequencies and produces an amplitudemodulation effect at higher frequencies. Comparison with a measured frequencyresponse function indicates that the proposed model has captured the principalcharacteristics of the sensor–actuator open-loop frequency response function up to 80 kHz.

Active damping of a beam using a physically collocated accelerometer and piezoelectric patch actuator

This paper presents a theoretical and experimental study of the active vibration control of a simply supported beam using a piezoelectric patch actuator and a physically collocated accelerometer. Direct velocity feedback (DVFB) control is used to attenuate unwanted vibrations in a given frequency band. The performance of the control system is presented in terms of the total vibrational kinetic energy of the beam and compared to the fundamental limitation, for the particular actuator, by way of a feedforward control analysis. Since the sensor and actuator are not collocated in the control sense, the control system is only conditionally stable. The stability is also influenced by the actual control system electronics and the transducer dynamics, which results in even lower stability margins. It is shown in this paper that for a given electronics system and transducer arrangement, improvements can be made by inserting a concentrated mass at the sensor location so as to cause an additional roll-off of the open-loop frequency response function at higher frequencies. This improves the stability margin of the overall control system and hence permits a higher control gain.

Rule-based autotuning based on frequency domain identification

A frequency domain procedure is proposed for the automatic tuning of proportional integral derivative (PID) controllers. The nonparametric open-loop frequency response function is estimated online (in closed loop), and simple discriminatory parameters are obtained, which enable appropriate tuning of the controller. For processes with some prior knowledge of the dynamics, the method removes the need for relay tuning or open-loop step response testing. If there is little or no prior knowledge of the process dynamics, relay or step response testing can be used initially, with the method then being used for the subsequent tuning. As part of the paper, a comprehensive comparison of existing rule-based tuning formulas is given using realistic plant examples.

Missile autopilot controller design using state transformations and optimal LQR techniques

The design of a missile autopilot controller which provides a fast and stable response to guidance commands, and which maintains this performance throughout the entire flight envelope, provides a challenging problem to flight control engineers. This paper considers the design of a lateral acceleration autopilot controller for a generic cruciform missile, and shows how full state feedback can be applied following the transformation of a physical state space model of the missile to a form where all the states are measurable and the introduction of lateral acceleration and pitch rate error states. This facilitates the successful application of the oft-disparaged optimal Linear Quadratic Regulator (LQR) control technique. In addition to the error states, the particular optimal control formulation makes use of fin position feedback. Integral action on the acceleration error state is introduced to ensure zero steady-state error in the presence of uncertainties and unmodelled dynamics. Autopilot controller design is performed directly in the discrete domain. Lateral acceleration time histories and open-loop frequency response functions for two flight speeds of a range of incidences are used to illustrate performance. System robustness is assessed using the open-loop gain and phase margins. Prior to the autopilot control law design study, a detailed discussion of the role, function and performance requirements of a missile lateral autopilot is given.

F-16 Flutter Suppression System Investigation Feasibility Study and Wind Tunnel Tests

A study was conducted to determine the feasibility of employing active controls on the F-16 to suppress wing- store flutter for several external store configurations. It was determined that the existing flaperons, with modifications to the integrated servoactuators, were effective in suppressing flutter. The F-16 flutter model was tested with active flaperons. Open-loop frequency response functions (FRF's) were successfully measured in the wind tunnel environment both with the feedback loop physically opened and with the loop closed. These measurements provided guidance in the selection of sensor locations and feedback control laws to suppress flutter. Control law variations were made to obtain the desired FRF characteristics. A 100% increase in dynamic pressure above the flutter dynamic pressure was demonstrated. IGHTER aircraft are required to carry a very large number of external store configurations. The probability is high that at least a small subset of these configurations will flutter within the desired operational envelope of the airplane. This probability is further increased as new stores are added to the operational airplane inventory. When wing-store flutter problems occur, the solution requires a modification of the airplane (usually a change in stiffness and weight) and/or a speed restriction which reduces the operational envelope of the airplane. Flutter suppression with active controls is another solution which has been investigated in recent years. Several approaches have been taken to design these sys- tems.1-3 One of the more promising approaches to the design of calibrated active control systems is the frequency response method. This approach is attractive because of the state of development of methods for computing oscillatory aerodynamic pressure distributions, because frequency response functions (FRF's) are experimentally measurable, and because the military specification for the stability of aeroservoelastic systems is based on the Nyquist criteria. This method was applied in a flutter suppression system (FSS) feasibility study4 for the F-4. The results of this study indicate that the milder flutter modes and the lower flutter frequencies associated with wing-store configurations could be relatively easily suppressed with active controls. The initial design approach for the active control system for the YF-17 semispan flutter model was the root locus method.5 However, a modified Nyquist approach was subsequently used.6 The Nyquist stability criteria has been applied extensively by Turner.7 The Nyquist criteria was employed as the principal design tool in the F-16 FSS investigations. For the system with negative feedback shown in Fig. 1, the transfer function for the closed loop system is

The characteristic locus design method

The classical work of Nyquist and Bode on the frequency-response analysis of scalar feedback systems leads to flexible and useful design procedures because it enables the conflicting requirements of stability and accuracy to be handled simultaneously via a single form of system representation—the open-loop frequency response function of a complex variable. State-space methods derive their elegance and power from the systematic exploitation of the algebraic and geometric properties of linear vector spaces. The basic idea underlying the Characteristic Locus Method developed here is the combination of the essence of these two approaches by exploiting the properties of linear vector spaces defined over base fields of functions of a complex variable. What then emerges is a general vector feedback theory in which the classical Bode-Nyquist technique is a special case, and from which a frequency-response based design technique called the Characteristic Locus Method is developed.