A Subspace Based Approach to the Design, Implementation and Validation of Algorithms for Active Vibration Isolation Control

By Gerard Nijsse

Abstract:

Vibration isolation endeavors to reduce the transmission of vibration energy from one structure
(the source) to another (the receiver), to prevent undesirable phenomena such as sound
radiation. A well-known method for achieving this is passive vibration isolation (PVI). In the
case of PVI, mounts are used - consisting of springs and dampers - to connect the vibrating
source to the receiver. The stiffness of the mount determines the fundamental resonance frequency
of the mounted system and vibrations with a frequency higher than the fundamental
resonance frequency are attenuated. Unfortunately, however, other design requirements (such
as static stability) often impose a minimum allowable stiffness, thus limiting the achievable
vibration isolation by passive means.
A more promising method for vibration isolation is hybrid vibration isolation control. This
entails that, in addition to PVI, an active vibration isolation control (AVIC) system is used
with sensors, actuators and a control system that compensates for vibrations in the lower
frequency range. Here, the use of a special form of AVIC using statically determinate stiff
mounts is proposed. The mounts establish a statically determinate system of high stiffness
connections in the actuated directions and of low stiffness connections in the unactuated
directions. The latter ensures PVI in the unactuated directions. This approach is called
statically determinate AVIC (SD-AVIC). The aim of the control system is to produce antidisturbance
forces that counteract the disturbance forces stemming from the source. Using
this approach, the vibration energy transfer from the source to the receiver is blocked in the
mount due to the anti-forces.
This thesis deals with the design of controllers generating the anti-forces by applying
techniques that are commonly used in the field of signal processing. The control approaches
- that are model-based - are both adaptive and fixed gain and feedforward and feedback
oriented. The control approaches are validated using two experimental vibration isolation
setups: a single reference single actuator single error sensor (SR-SISO) setup and a single
reference input multiple actuator input multiple error sensor output (SR-MIMO) setup.
Finding a plant model can be a problem. This is solved by using a black-box modelling
strategy. The plants are identified using subspace model identification. It is shown that
accurate linear models can be found in a straightforward manner by using small batches of
recorded (sampled) time-domain data only. Based on the identified models, controllers are
designed, implemented and validated.
Due to resonance in mechanical structures, adaptive SD-AVIC systems are often hampered
by slow convergence of the controller coefficients. In general, it is desirable that the SD-AVIC
system yields fast optimum performance after it is switched on. To achieve this result and
speed up the convergence of the adaptive controller coefficients, the so-called inverse outer
factor model is included in the adaptive control scheme. The inner/outer factorization, that has to be performed to obtain the inverse outer factor model, is completely determined in
state space to enable a numerically robust computation. The inverse outer factor model is also
incorporated in the control scheme as a state space model. It is found that fast adaptation
of the controller coefficients is possible.
Controllers are designed, implemented and validated to suppress both narrowband and
broadband disturbances. Scalar regularization is used to prevent actuator saturation and an
unstable closed loop. In order to reduce the computational load of the controllers, several
steps are taken including controller order reduction and implementation of lower order models.
It is found that in all experiments the simulation and real-time results correspond closely for
both the fixed gain and adaptive control situation. On the SR-SISO setup, reductions up to
5.0 dB are established in real-time for suppressing a broadband disturbance output (0-2 kHz)
using feedback-control. On the SR-MIMO vibration isolation setup, using feedforward-control
reductions of broadband disturbances (0-1 kHz) of 9.4 dB are established in real-time. Using
feedback-control, reductions are established up to 3.5 dB in real-time (0-1 kHz). In case of
the SR-MIMO setup, the values for the reduction are obtained by averaging the reductions
obtained in all sensor outputs.
The results pave the way for the next generation of algorithms for SD-AVIC.

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