Laser communication, renowned for its high transmission rates and substantial information capacity, finds extensive applications in satellite communication, military communication, and other related fields. The establishment of a stable and persistent communication link in complex and dynamic environments is pivotal for the realization of laser communication. This link's establishment and maintenance are facilitated through the deployment of a pointing, acquisition and tracking system. Among the pointing, acquisition and tracking system's components, the coarse tracking system plays a vital role, performing functions such as line of sight alignment, target tracking, and isolating external disturbances from the carrier. However, in practical operations, the coarse tracking system is susceptible to internal nonlinear characteristics, including frictional torque, load imbalance, and shaft coupling, as well as external disturbances, all of which contribute to a degradation in control accuracy. To address these challenges, a comprehensive modeling and multi-objective complementary control method is proposed. This method aims to mitigate the adverse effects of friction on the low-speed control performance of the coarse tracking system in laser communication and to transcend the mutual constraints between tracking performance and disturbance rejection inherent in traditional control methods. The frequency responses derived from both sine sweep and pseudo-random sequence measurements are integrated to enhance the accuracy of the overall frequency response characterization. (Fig.3). By employing the Hankel matrix method, the system order and parameters are identified, accompanied by a quantitative analysis of the model uncertainty. Following this, the Stribeck friction model is formulated for the coarse tracking system (Tab.1), enabling the design of a friction model-based feedforward compensation control scheme (Fig.7), which significantly mitigates the dead zone problem in low-speed tracking scenarios (Fig.9). Finally, within the framework of multi-objective complementary control (Fig.11), a controller for the coarse tracking system is designed through the implementation of mixed-sensitivity control methodology(Eq.28). The designed controller addresses the inherent trade-off between system performance and robustness, demonstrating superior characteristics when compared with conventional PID, disturbance observer, and active disturbance rejection control through comprehensive comparative analysis. The comparative results show that the multi-objective complementary control reduces the settling time by 26.8%, 38.8%, and 35.4% compared to PID, disturbance observer, and active disturbance rejection control, respectively, and decreases the overshoot by 46.6%, 31.9%, and 35.6% (Tab.2). Compared to PID, disturbance observer, and active disturbance rejection control, the multi-objective complementary control reduces the maximum error by 25.5%, 18.9%, and 12.3%, respectively, and lowers the root mean square error by 14.8%, 13.3%, and 14.2% when tracking a 0.5 Hz sinusoidal signal (Tab.3). Additionally, it exhibits stronger disturbance rejection capability within the working bandwidth of 10-100 rad/s (Fig.23). The experimental results demonstrate that the proposed comprehensive modeling approach significantly enhances the modeling accuracy of the coarse tracking system. Furthermore, the multi-objective complementary control strategy effectively improves both tracking performance and disturbance rejection capability of the system simultaneously. To improve control performance, comprehensive modeling is conducted for both the linear and nonlinear characteristics of the azimuth axis in the coarse tracking system. For the linear dynamic part, a combination of the low-frequency segment from a sinusoidal sweep signal and the medium-to-high frequency segment from a pseudo-random sequence is employed to achieve a more accurate frequency response. The model order and parameters are then identified using the Hankel matrix-based identification method. For the nonlinear characteristics, the Stribeck model is employed for friction modeling, and the parameters are identified. A friction compensation feedforward controller is designed, which improves the low-speed reversal performance. To resolve the conflict between tracking accuracy and disturbance rejection in conventional control approaches, the multi-objective complementary control strategy is proposed for the coarse tracking system in laser communication. This method effectively improves both tracking performance and disturbance suppression capabilities, and is implemented through a mixed-sensitivity control framework. Experimental results demonstrate that the proposed method outperforms PID, disturbance observer, and active disturbance rejection control in terms of control performance, tracking accuracy, and disturbance rejection capability, thereby validating the feasibility and effectiveness of the approach.