## 1 Introduction  
Due to its high pointing accuracy, strong resistance to electromagnetic interference, and low operational costs, electro-optical equipment is widely used in various fields, such as range measurement [1], military reconnaissance [2], and laser defense weapons [3]. The servo system of electro-optical equipment is a typical electromechanical servo system with flexible modal characteristics [4; 5], whose bandwidth is limited by the resonant frequency of the tracking frame [6]. Generally, the shear frequency of the speed loop ranges from 30% to 50% of the lock-in frequency, and the shear frequency of the position loop ranges from 10% to 20% of the lock-in frequency [7]. This bandwidth limitation also dictates the tracking performance limits of electro-optical equipment. When tracking ultra-high-speed and highly maneuverable targets, the desired tracking accuracy cannot be achieved through series correction alone [8]. Composite control is a primary means to improve the tracking performance of electromechanical servo systems. By integrating with technologies such as dynamic programming, Kalman filtering, delay compensation, and multi-source information fusion, advanced control algorithms have been developed and widely applied in industrial servos, robotics, and aircraft control [9; 10]. Unlike these applications, electro-optical equipment is a follow-up servo system where the information acquired during tracking is the deviation rather than angular input, allowing only for equivalent composite control, such as speed lag compensation and acceleration lag compensation [11]. The performance of equivalent composite control has been validated in multiple domestic range measurement devices, leading to the development of coaxial tracking technology based on multi-source information fusion [12]. However, during the development of electro-optical equipment, it was found that the speed feedforward generated by coaxial tracking can easily cause instability in the servo system. This issue is directly related to the robustness loss caused by equivalent composite control and has not received sufficient attention in past research [8; 11; 12]. Robust and optimal design methods, which transform control system design into rigorous mathematical optimization problems, have been a hot topic in high-performance servo system design in recent years. Methods such as \(H_{\infty}\) mixed sensitivity shaping, \(\mu\) synthesis, and GKYP (Generalized KYP Lemma) [13; 14; 15; 16; 17; 18], although currently limited by system uncertainty measurements, provide a valuable approach by considering factors such as system tracking performance to effective inputs, response to external noise errors, and disturbance suppression capabilities. Studies combining classical Disturbance-Observer-Based Control (DOBC) design with robust control design, deliberately creating discrepancies between nominal and actual models to enhance torque resistance suppression while analyzing robustness loss, have optimized the control structure [19; 20; 21]. Tracking precision of high-speed targets has always been a paramount metric in the design of electro-optical equipment servo systems. Within limited bandwidths, employing series correction alone often fails to achieve the desired velocity and acceleration quality factors. Thus, incorporating equivalent composite control (coaxial tracking) can enhance the system's tracking performance. However, in modern warfare scenarios characterized by complexity and uncertainty, solely focusing on steady-state precision during the design process proves insufficient. Dynamic response capability and robustness should equally be crucial considerations in the design process. In this paper, we propose a novel equivalent composite control structure for electro-optical equipment, examining the improvements in tracking performance, robustness loss, and impacts on the speed loop from various perspectives, and presenting a balanced choice with optimal performance and robustness.