## 1 Introduction  
During the last decade, active vibration cancellation (AVC) has been widely investigated for achieving vibration attenuation in the aerospace and automotive fields [1, 2, 3]. Especially, AVC using piezoelectric (PZT) patches [4, 5] has attracted attention due to its advantages of light weight, compact size, and low cost [6, 7]. In recent years, many efforts have been made in terms of actuator placement to facilitate AVC applications using PZT patches [5]. Utilizing the optimal actuator placement, the AVC effect for each concerned mode cannot be ensured in many practical applications [8]. Therefore, several measures should still be taken to ensure the performance of AVC.  
Controllability and observability analyses are helpful to ensure the AVC effect, which was proved by [PERSON] et al. [9]. [PERSON] et al. [10] emphasized that the controllability and observability of AVC are influenced by the size and location of the actuators. [PERSON] et al. [11] utilized spatial controllability/observability to determine optimal orientations of PZTs and ensured the AVC effect. [PERSON] et al. [12] pointed out that the AVC effect is mainly affected by unobserved model dynamics at the location of piezoelectric sensors. In addition, [PERSON] et al. [13] summarized that a misplacement of piezoelectric patches can lead to a lack of observability and controllability. Considering the lack of observability and controllability, majority studies mainly focused on high frequency spillover induced by the uncontrolled mode [14, 15, 16]. [PERSON] et al. [14] demonstrated that the high frequency spillover of AVC is mostly determined by the uncontrolled mode.  
[PERSON] et al. [15] weighted several uncontrolled modes to prevent the spillover of AVC. For spillover reduction of the modes, [PERSON] et al. [16] proposed an optimal sensor placement to ensure vibration reduction in the controlled mode. Furthermore, [PERSON] et al. [17] noted that the vibration of a smart structure may be aggravated in the controlled mode. The aggravated vibration does not benefit the actual suppression of vibration and noise. However, only a few studies considered the aggravated structural vibration induced by AVC.  
In order to ensure the AVC effect, the mechanism of aggravated vibration is revealed, which is related to the location of PZT. When the positions are assigned, the structural modes can be divided into controllable and uncontrollable modes. Based on the open-loop and closed-loop energies of AVC, a criterion for the selection of controllable modes is proposed. When AVC is implemented at the selected controllable mode, vibration attenuation can be achieved. Meanwhile, the uncontrollable modes should be excluded during the implementation of AVC to avoid aggravated vibrations.  
The rest of the article is organized as follows. In Section 2, the dynamic model of the smart plate is built. In Section 3, the criterion is presented to specify controllable and uncontrollable modes. In Section 4, simulations for each concerned mode are carried out to verify the theoretical analyses. In Section 5, typical experiments are performed to further verify the selected controllable and uncontrollable modes. Finally, several conclusions are drawn.