## 2 The Active Vibration Isolation System
### Control System  
Diagrams of the adaptive control system and the hardware are shown in Figure 3a,b respectively. The input to the control system is the reference signal, \(x(n)\), as can be seen in Figure 3a. The raw output from the tachometer contains the fundamental frequency (first order) and harmonics (higher orders). However, half orders of the engine speed are necessary because the engine is a four-stroke diesel. A circuit to generate half orders was designed using a filter to allow only one pulse out of every two pulses to pass. This is shown in Figure 1b and is marked B. The spectrum of the resulting signal together with that from the original signal are shown in Figure 4 for an operating speed of 1500 rpm (which corresponds to the 1 st harmonic at a frequency of 25 Hz). The signals are passed through a low-pass filter set to 200 Hz, which is the maximum frequency considered in the control process. Figure 3: (**a**) A block diagram of the adaptive control system and (**b**) a schematic diagram of the control system showing the hardware. Figure 2: (**a**) Schematic diagram and (**b**) photograph of the inertial actuator. The adaptive control system, whose block diagram is in Figure 3a, is a six-input and six-output control system based on the x-LMS algorithm [24,25]; \(x(n)\) is the reference signal, \(W(z)\) is the controller filter, \(\mathbf{y}(n)\) is the controller output vector, \(S(z)\) is the secondary path, \(\mathbf{d}(n)\) is the desired signal vector which consists of vibration responses from the six error sensors without control, \(\mathbf{e}(n)\) is the error signal vector which consists of vibration responses from the six error sensors after control, and \(\mathbf{x}^{\prime}(n)\) is the vector of the reference signal after being filtered by the estimated secondary path, \(\hat{S}(z)\). As shown in Figure 3b, the outputs of the controller pass through band-pass filters and power amplifiers to drive the six inertial actuators. Outputs from the six error sensors pass through charge amplifiers and low-pass filters, and are fed into the controller as error signals. An ADI DSP-based hardware system is used as the controller. As discussed in [11], the performance of an active vibration control system depends largely upon the transfer functions of the secondary paths, so the effects of secondary paths must be compensated for by passing the reference signal through the estimated secondary path filters, which are denoted by \(\hat{S}(z)\) in Figure 3a. A secondary path is the path between a controller output signal and an error signal, including the D/A (digital-to-analogue) converter, band-pass filter, power amplifier, actuator, physical system from the actuator location to the error sensor position, the error sensor itself, charge amplifier, low-pass filter and A/D (analogue-to-digital) converter. The impulse responses between the first inertial actuator to all six error sensors are shown in Figure 5a. It can be seen that the driving point impulse response function (IRF) is much larger than the transfer IRFs, which means that the secondary paths are weakly coupled. This, in turn, means that a decentralized control system could be implemented, drastically reducing the complexity.