Abstract This paper introduces the scheme, composition, basic working principle, and main parameter design of the DS-02 electric servo system. Simultaneously, the no-load linear region loop and no-load nonlinear control loop of the servo system are calculated and analyzed. In particular, the nonlinear element that mainly affects the speed saturation of the servo system is studied using an accurate describing function. This calculation and analysis of the nonlinear control loop can serve as a reference for relevant technical personnel in the field of automatic control. Keywords: servo system, design, calculation. 1. Overview The DS-02 electric servo system (hereinafter referred to as the servo system) is a medium-power fast tracking system composed of a servo amplifier and an electric servo mechanism. It can integrate and amplify the input signal and the position feedback signal and speed feedback signal of the servo system, and perform angle tracking and maximum angle limiting on the integrated and amplified signal, thereby manipulating the deflection of the aircraft's control surfaces to achieve the purpose of stabilizing and controlling the aircraft's flight. The main technical indicators of the servo system are as follows: a. Maximum control current: 150±10mA; b. Zero position: not greater than 12°; c. Maximum working angle: ± (15°±1°); d. The transmission ratio is ± (1. ± 4.5) / ± 500mV; e. The linear region is ± (1.25. ± 0.15). The dynamic characteristics (within the linear region) should meet the following requirements: the settling time is not greater than 120ms, the overload is not greater than 10%, and the number of oscillations is not greater than 2. g. The maximum no-load speed is not less than 60 s. h. The maximum load torque is not less than 78.4 N·m. i. The reliability R = 0.9956. j. Power supply: DC 2g. st~. V and ± (15±0.1)V. 2 Scheme Selection According to the technical specifications of the rudder system, it can be seen that the control power is small, the output power is not large, and the speed requirement is not high. Therefore, it is very suitable to use a magnetic powder clutch as the control element of the rudder system. In the design of the rudder system, in the past, a servo system with a terminal switch protection device was usually used. The static characteristics of this servo system are shown in Figure 1. In Figure 1, the input signal u must be within the range, that is, the output angle cannot be equal to or greater than the maximum angle S. Therefore, this servo system can only be used under the condition that the value does not exceed S. Otherwise, the servo system will be unstable and the servo mechanism will be damaged. Figure 2 shows the static characteristics of the limiting servo system. This type of servo system does not require a terminal switch protection device. As shown in Figure 2, this servo system has no limit on the size of the input signal, that is, even if the output angle exceeds the maximum angle S, the servo system will still work normally, thus solving the problem of unstable operation of the servo system under large input signals and protecting the servo mechanism. In summary, in order to meet the technical requirements of the rudder system and ensure that the designed rudder system is simpler, more economical, and more reliable, this rudder system adopts a limiting magnetic powder clutch type electric servo system. 3 Composition and Basic Working Principle 3.1 Composition As shown in Figure 3, the rudder system consists of a hybrid amplifier circuit, a limiter, a power amplifier, a magnetic powder clutch, a motor, a tachogenerator, a reducer, a speed increaser, and a potentiometer. 3.2 Basic Working Principle The input signal and the position feedback signal and speed feedback signal of the rudder system are amplified by the hybrid amplifier circuit and then drive the power amplifier to work. Then, a certain control current is supplied to the magnetic powder clutch by the power amplifier. Under the action of this control current, the magnetic powder clutch operates. At the same time, the torque output by the motor is transmitted to the output shaft through the reducer. When the input signal is zero, the control current is zero, and neither of the two magnetic powder clutches operates. At this time, the output torque of the motor cannot be transmitted to the output shaft, and the output shaft does not deflect. When the input signal is a positive voltage, the control current is only output to one of the magnetic powder clutches. This magnetic powder clutch operates, transmitting the torque output by the motor to the output shaft, causing the output shaft to deflect in one direction; conversely, when the input signal is a negative voltage, the other magnetic powder clutch operates, causing the output shaft to deflect in the other direction. To stabilize the output angle of the rudder system and make the output angle proportional to the input signal, a potentiometer is used for position feedback. To make the rudder system work stably and improve the dynamic quality of the rudder system, a tachogenerator is used for speed feedback. 4 Design of Rudder System Parameters 4.1 Rudder System Block Diagram As shown in Figure 4. This block diagram ignores the influence of minor factors such as hysteresis, gear backlash, and other very small time constants. 4.2 Calculation and selection of rudder system parameters 4.2.1 KI Based on the transmission ratio of 1/500mV and the output angle limit value of ±1/5, we can get KI=1.15 4.2 2 K 2, [align=center] Figure 4 Block diagram of DS-02 electric rudder servo system[/align] When the input signal S is given, the corresponding output angle is, and the static relationship between them is. According to the requirement of transmission ratio 1/1500mV, we can get K 2= 0.77 4.2.3 K3 According to the requirements of dynamic characteristics, a suitable K3 can be selected. Here, K3=0.09 is sufficient to meet the requirements. 5 Calculation and analysis of the stability of the rudder system in the no-load linear region loop Simplify Figure 4 into the form shown in Figure 5, and substitute each known parameter into the block diagram. According to Figure 5, the closed-loop transfer function can be obtained as follows. From equation (1), it can be seen that the system is a third-order linear system in a small range. Its closed-loop characteristic equation is: According to the Rauss criterion, this system is stable. Because the coefficients of the characteristic equation have the same sign, all roots of the characteristic equation are in the left half of the complex plane. 6 Calculation and analysis of the dynamic characteristics of the no-load linear loop of the rudder system Suppose that the rudder system is under zero initial conditions, and under the action of a unit step signal "k = 10", the transient process of the rudder system is T. k = 1 (t) is transformed by Laplace as: From equation (6), it can be seen that the oscillation amplitude of the third term in the equation is very small, and its influence on S can be ignored. The main factor affecting S (t) is the second term in the equation, whose attenuation coefficient is 44.71 and the attenuation time constant is 22.37 ms. This term can attenuate 96% at 67.1 lms. Therefore, the oscillation of the system transient process is very small. 7 Calculation and analysis of the stability of the no-load nonlinear loop of the rudder system Among the nonlinear factors existing in the rudder system loop, the limiting characteristic of the servo amplifier has a negligible effect on the system, while the speed saturation characteristic is the main factor affecting the system. Therefore, Figure 5 can be transformed into Figure 6 to consider the equivalent transfer function of the speed saturation characteristic (including the integral plateau). In order to facilitate the analysis using the describing function method, Figure 6 can be transformed into Figure 7. From Figure 7, the open-loop transfer function of the linear part of the system can be obtained as 8. Conclusion The parameters of the rudder system are designed according to the technical requirements. The speed feedback coefficient of the system has a large range of variation, which provides a large range of motion for the dynamic characteristics of the servo system. In addition, this paper focuses on the calculation and analysis of the no-load linear zone loop and the no-load nonlinear control loop. Practice has proven that the designed rudder system is stable and meets the technical requirements. References [1] Xie Ziliang, Chen Zhengfu "Design of HT-880314～DD-02C Electric Servo System and its Control Circuit" published in August 1988 [2] Chen Zhengfu "Nonlinear Characteristics of Memory-type Linear Components at Output Saturation" 1982 8043 Conference Exchange Materials Click here to download the original text