## 1 Introduction
They obtained the relationship between the size of the quiet zone and the number of secondary sound sources and the wavelength of secondary sound sources in two and three dimension cases [23]. [PERSON] et al. proposed an amplitude matching algorithm for multizone sound field control, which produces the expected amplitude distribution in the designated region by alternating the direction method of multipliers, without paying attention to phase distribution [24]. There are also some experts who have studied the application of personal audio systems. [PERSON] et al. studied the application of the ACC method to a headrest [25]. [PERSON] et al. conducted some research on the application of personal audio systems to mobile phones [26]. [PERSON] et al. also put personal audio systems into a car with two loudspeaker arrays [27]. Different from the method described in the literature [27], [PERSON] et al. proposed to fix loudspeaker arrays on the ceiling of a car compartment in order to produce separate high-frequency listening regions in the front and rear seats of the car compartment [28]. They also investigated the geometric size design method for ceiling-mounted loudspeaker arrays and target sound pressures' selection method. Compared with the system in the literature [27], the system proposed by [PERSON] et al. shows obvious performance improvement in the frequency range of 1-4 kHz. Based on an line loudspeaker array mounted on a flat-screen TV in the form of a bar loudspeaker, [PERSON] proposed two kinds of sound field control systems for home applications that are real-time. One kind of system is a personal audio system that makes users at different positions experience independent sound effects by reducing the mutual interference of different sound zones; another kind of system can exert an influence on the spatial audio scene [29]. The sound property considered by most existing sound field control technologies is sound pressure. Additionally, many of the sound field control technologies proposed by researchers are improved techniques based on sound pressure. Sound pressure and particle velocity can be used to describe sound [30]. Additionally, it is pointed out in [31] that when loudspeakers are not evenly placed, the loudspeaker signal obtained by controlling the sound pressure of a single region is less stable than the loudspeaker signal obtained by controlling the particle velocity of a single region. Because in real life, many loudspeaker arrays are not evenly placed, particle velocity should be considered in addition to sound pressure in the design of sound field control methods. On the basis of traditional methods,a sound field control method based on sound pressure and particle velocity is introduced in order to reconstruct a sound field in the bright zone better, reduce acoustic energy in the dark zone, and pay attention to the stability of the system. The main contributions of this paper are as follows: based on the traditional sound field control technology, a new sound field control method is proposed by introducing particle velocity. The proposed method attempts to minimize the reconstruction error in the bright zone and minimize the loudspeaker array effort while controlling the sound pressure and particle velocity in the dark zone. The proposed method attempts to control or optimize acoustic contrast, reconstruction error, and array effort at the same time. The model of the proposed method contains three weight factors; this paper introduces their functions and gives their selection methods. The content of this paper is arranged as follows: Section 1 mainly describes the development status of sound field control technology. Section 2 describes three existing sound field control technologies and analyzes their advantages and disadvantages. Section 3 introduces the model of this new method and parameter selection method of the model. Section 4 introduces the comparison experiment between traditional methods and the proposed method, and analyzes and discusses the results. Section 5 gives the conclusions.