# A Feasibility Study of the Use of PZT Actuators for Active Control to Enrich Engine Sound
## 2 Active Sound Enrichment Using PZT Actuators
### Novel ASE System Using a PZT-Plate Actuator and ASE Algorithm  
A novel ASE system is proposed and is displayed in Figure 2 which is a block diagram of the whole system implemented in a car. It shows the digital signal processor to accommodate the ASE algorithm, the input and output signal flows, the necessary electronics and the PZT-plate actuator. The PZT-plate actuator is considered as a secondary actuator that generates sound to supplement poor engine sound. The PZT actuator was bonded on a plate at the mounting location of the rear mirror of a car, as illustrated in Figure 2.  
In this system, the primary path is considered as the acoustic relationship between the primary source, which is the explosion in the engine cylinders of a car, and the microphone installed at the driver's ear location. The secondary path is defined as the electro-acoustic relationship between the PZT-plate actuator and the microphone. The ASE algorithm proposed in this study is a purely feedforward control form, as shown in the dashed box in Figure 2. The proposed algorithm is devised to make the sound at the driver's ear equal to the pre-defined target sound at a certain engine RPM. Usually, the target sound is strictly defined by a professional sound designer to satisfy the required sound quality of a specific car. (However, a reasonable target sound was used for only  
Figure 1: Radiated sound from the combination of a rectangular PZT actuator and a rectangular plate propagating to the ear location. (**a**) Three-dimensional view. (**b**) Cross-section at the middle of the combination in the y-axis. three engine orders, say C3, C5, and C6, in this study to investigate the feasibility of this proposed approach.) As the target sound \(c(n)\) is pre-defined by an RPM-amplitude table of specific engine orders to supplement poor engine sound, once the engine RPM is given, the proposed ASE algorithm automatically generates the control signal \(u(n)\) in accordance with the pre-defined target sound table. However, the control filter \(A(z)\) must have an ability to predict the inverse property of the secondary path to generate correct target sound at the driver's ear in real-time environment. Thus, in this section, the proposed ASE algorithm is described with theoretical symbols and notations to clarify the operation of this approach. For convenience, all symbols are represented in the discrete form using variables of \(n\) in time-domain and \(z\) in z-domain. The ASE algorithm in Figure 2 can be summarized in a simple block diagram, as depicted in Figure 3, where \(A(z)\), \(S(z)\), \(d(n)\), and \(y(n)\) are the inverse control filter, actual secondary path, disturbance signal (original engine sound), and output signal (supplemented sound by the ASE), respectively. With a specific engine order at a certain RPM, the proposed ASE algorithm endeavors to make the order sound level in the error signal \(e(n)\) equal to the target sound \(c(n)\). The error signal \(e(n)\) can be written, from the block diagram in Figure 3, as:  
\[ \begin{array}{ll}e(n)&=d(n)+y(n)\\ &=\ d(n)\ +\ A(z)S(z)c(n).\end{array}  \tag{3}\]  
Assuming that the original engine sound \(d(n)\) is poor and the target sound \(c(n)\) is much greater than \(d(n)\), Equation (3) can be expressed as:  
\[e(n)\approx A(z)S(z)c(n). \tag{4}\]  
Figure 3: Simply expressed block diagram of the ASE algorithm. Figure 2: Block diagram of the proposed ASE system using a PZT actuator bonded on a plate at the mounting location of the rear mirror of a car. Furthermore, provided that the control filter \(A(z)\) is identical to the inverse of the secondary path \(S(z)\), Equation (4) can be given by:  
\[e(n)\approx c(n)\,\quad\text{if }A(z)\approx S^{-1}(z). \tag{5}\]  
This indicates that the sound \(e(n)\) at the driver's ear will follow the target sound \(c(n)\) perfectly, if \(A(z)\) is the exact inverse of \(S(z)\). However, in practice, this cannot be achieved with a stable \(A(z)\) since \(S(z)\) in the proposed system is non-minimum phase.