Andreas H. von Flotow

Modelling of Piezoelectric Actuator Dynamics for Active Structural Control

The paper models the effects of dynamic coupling between a structure and an electrical network through the piezoelectric effect. The coupled equations of motion of an arbitrary elastic structure with piezoelectric elements and passive electronics are derived. State space models are developed for three important cases: direct voltage driven electrodes, direct charge driven electrodes, and an indirect drive case where the piezoelec tric electrodes are connected to an arbitrary electrical circuit with embedded voltage and current sources. The equations are applied to the case of a cantilevered beam with surface mounted piezoceramics and indirect voltage and current drive. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with indirect voltage drive.

Design of passive piezoelectric damping for space structures

Passive damping of structural dynamics using piezoceramic electromechanical energy conversion and passive electrical networks is a relatively recent concept with little implementation experience base. This paper describes an implementation case study, starting from conceptual design and technique selection, through detailed component design and testing to simulation on the structure to be damped. About 0.5 kg. of piezoelectric material was employed to damp the ASTREX testbed, a 5000 kg structure. Emphasis was placed upon designing the damping to enable high bandwidth robust feedback control. Resistive piezoelectric shunting provided the necessary broadband damping. The piezoelectric element was incorporated into a steel flextensional device in order to concentrate damping into the 30 to 40 Hz frequency modes at the rolloff region of the proposed compensator. The effective stiffness and damping of the flextensional device was experimentally verified.

Adaptively tuned vibration absorber

An apparatus for absorbing vibrations in a structural member, such as in an aircraft fuselage, has first and second plates for attaching to the structural member. A mass, which is suspended between the plates, includes a first block connected to the first plate by a first spring and a second block connected to the second plate by a second spring. The springs may be formed by metal straps which allow the mass to move along one axis or by rods which allow two axis movement of the mass. One sensor produces a signal indicating vibration of the structural member and another sensor produces a signal indicating vibration of the mass. A mechanism connected to the first and second block responds to a control signal by varying a distance between the first and second block to alter stiffness of the first and second springs. A control circuit receives the signals from the sensors and produces the control signal which causes the mechanism to alter the spring stiffness so that the spring and the mass resonate to absorb vibration of the structural member.

Active Modification of Wave Reflection and Transmission in Flexible Structures

A theory for active control of elastic wave propagation in structures is developed. Attention is focused on active modification of the scattering behavior of discrete locations in a structural network. The wave mode input/output relation at a structural junction containing control actuators can be altered in two ways. First, the closed loop reflection and transmission coefficients can be specified, and the necessary feedback to achieve these coefficients determined. Second, an optimal wave controller can be formulated which maximizes the average power dissipation at a junction. If the open loop structure is stable, then the optimal control guarantees stability, since energy is actively dissipated at the junction. Sample controllers are derived and simulated for a free-free beam to demonstrate the techniques and indicate the achievable performance.

Electronic controller for an adaptively tuned vibration absorber

An apparatus for absorbing vibrations in a structural member has a mass suspended between two mounting plates by a separate springs. The mass has two sections and a mechanism for adjusting the spacing between the sections to alter the spring stiffness. Two sensors produce first and second signals representing the vibration of the structural member and the mass. The mechanism is operated by a controller that includes separate filters for the first and second signals in which each filter has a center frequency that is tuned by a clock signal. The phase comparator produces a phase output signal indicating a phase relationship between signals from the two filters and the control signal for the mechanism is produce in response to the phase output signal. A phase locked loop produces the clock signal for tuning the filters in response to a comparison between one of the first and second signals and a signal from one of the filters.

Blade vibration control in turbo-machinery

A method for reducing blade vibration in turbo-machinery is described. The method involves inserting flow obstructions and/or gas injections upstream of vibrating blades in such a manner that power flow into the blades is reduced by means of cancellation within a modal power integral.

Pointing dynamics of gimbaled payloads on flexible spacecraft

Following the failure of the third of six gyros, the system momentum test was enabled on November 20, 1992. With the test enabled, a soft gyro failure in a three-gyro configuration will trigger a safemode entry to either the Zero Gyro Sunpoint safemode in the flight computer or the hardware sunpoint capability using the Pointing and Safemode Electronics Assembly along with the retrieval mode gyros. The safety provided by the system momentum test will be even more critical if the HST is routinely operated in a three-gyro configuration after the first Hubble servicing mission, as is currently planned.

Trajectory Design, Feedforward, and Feedback Stabilization of Tethered Spacecraft Retrieval

This paper focuses on the final 2 km of retrieval of a tethered subsatellite (TSS) to the Space Shuttle. From each initial condition a nominal retrieval trajectory is determined, which is implemented with the tether reel and requires nominally zero thrusting. The retrieval dynamics of the TSS are unstable, and open loop retrieval by itself is not practical. Consequently, a loop structure is designed that combines feedforward information with thruster actuated feedback stabilization. The tether-normal thrusters mounted on the subsatellite are used to stabilize the in-plane and out-of-plane dynamics along the precomputed trajectory. A Kalman filter is used to estimate pitch and pitch rate from a noisy pitch sensor. This whole design yields fast retrievals, limited primarily by constraints on docking speed and tether tension. Thruster fuel use is driven by sensor noise, rather than by the need to remove system angular momentum. Numerical results clearly indicate that, to limit fuel use, system pitch attitude must be measured with a resolution much better than the 2 deg currently planned.

Evaluation of actuation schemes used for acoustic attenuation of vibrating surfaces

This paper compares three actuation schemes to attenuate turbulent boundary layer sound radiated into the cabin through an aircraft fuselage. Two actuation schemes make use of piezoelectric materials and are compared with conventional electromagnetic voice coil actuation. Volume displacement of electromechanical actuators is typically proportional to either volts or amperes. Comparison between actuators can be problematic since drive impedances vary greatly. This paper presents a reliable method to compare actuator power using a transfer function of volume per square root of power. This power consumption curve is useful in direct comparison of actuator stroke capability and spacing requirements.

High-bandwidth positioning control of small payloads mounted on a flexible structure

This paper considers the problem of high-bandwidth positioning and pointing of a small mass mounted on a flexible structure. A potential application would be the positioning of mirrors in a space-based interferometer. For high-performance control it is a general rule that a sufficiently accurate model of the plant is needed in the control bandwidth, particularly at crossover. Determining a sufficiently accurate model of a flexible structure over a broad frequency band is a very difficult problem. This paper points out that, for small payloads, the plant transfer function from control actuation to sensing is only lightly perturbed from what it would be if the structure was rigid. The paper identifies a bound on the gain and phase perturbations of the plant as a function of the ratio of the payload mass to modal mass of the structure. It is shown that, when this ratio is small enough, a high-performance stable controller can be designed without further consideration of the structural dynamics. Experimental results are presented that quantitatively support the predictions.