# Variable Structure PID Controller for Satellite Attitude Control Considering Actuator Failure
## 1 Introduction  
With the rapid development of the aerospace industry, more and more attention has been paid to the high precision attitude control for satellites. To ensure high precision, high reliability, and a fast convergence rate of the satellite, the control system of the satellite must have sufficient control capability. At present, many researchers have studied the basic theories and problems of satellite attitude control [1; 2; 3; 4; 5; 6]. As a commonly used method in satellite attitude control, PID control can achieve the closed-loop control system, reaching a steady state, and it has the advantages of a simple structure and easy engineering implementation. However, the control accuracy of PID control is relatively low, which often cannot meet the requirements of current missions. Furthermore, in order to ensure the stability of the satellite attitude control system under actuator failure (which is quite often in space missions and is one of the major reasons for mission failures), it is necessary to enhance the system fault tolerant capability to actuator failures. Hence, it is necessary to modify current PID controllers to meet the precision, reliability, and fast convergence rate requirements. For the PID control method, [PERSON] [7] designed a low-complexity structured H-infinity controller for flexible satellite attitude control considering interference suppression. [PERSON] [8] designed an adaptive sliding mode integral controller for the control of the robotic arm of the spacecraft and used a PID-type integral sliding mode control surface to reduce the steady-state error. [PERSON] [9] designed a fuzzy PID control algorithm according to the characteristics of the three-axis stable zero-momentum wheel. The authors used a PID control algorithm to manipulate the satellite attitude, but the result could not achieve the desired control accuracy. In summary, researchers made some improvements to the PIDcontrol algorithm, but there is still a lack of study on a fault-tolerant control algorithm with a good convergence rate, combined with a PID control algorithm. For the fault-tolerant control method of satellite attitude control, [PERSON] [10] designed a satellite attitude fault-tolerant control algorithm for an agile satellite attitude control system, which can achieve agile satellite attitude control and accurately output control torque, with the purpose of fast maneuver and high-precision stability attitude under fault conditions. [PERSON] [11] designed an adaptive fault-tolerant attitude tracking control algorithm based on a neural network for the case of partial failure or even complete failure of the spacecraft actuator. [PERSON] [12] proposed an adaptive fault-tolerant control method based on a disturbance observer for the problems of actuator failure and space environment disturbance in a flexible satellite attitude control system. These works only focus on the problem of satellite control system fault tolerance and anti-jamming ability, but they do not pay attention to the system convergence rate. A variable structure controller is one of the main methods to improve the system convergence rate. [PERSON] [13] designed a two-stage pulse variable structure phase plane partition attitude controller for an integrated control system of a navigation satellite four-inclined chemical propulsion. [PERSON] [14] designed a variable structure controller based on error quaternion and error angular velocity for the large-angle attitude maneuver problem of agile satellites. For the control problem of satellite attitude, a variable structure control method is used to achieve higher precision control compared with PID control, but most works do not pay attention to the fault tolerant issue. In addition, the PID fault-tolerant control method has been applied to the field of electric vehicles [15], servo motors [16], quadcopter drones [17], and so on. For the variable structure PID control method, it can also be applied to stepper motors [18], robots [19], and so on.