With the wide application of robots, position control has become a hot topic. The robot is a nonlinear control system with strong coupling characteristics. Due to the influence of modeling imprecision and external disturbance, the precision of robot end-effector is always a difficult problem. At present, the control of joint robot usually separates the robot from the driving motor. Only the robot dynamics is considered, and the simulation analysis is done at the position-loop level, without considering the actual driver model, which is not easy to be implemented in engineering. The driving motor of joint robot is usually permanent-magnet synchronous motor (PMSM). The control of it is always a hot topic due to its multi-variable and strong coupling characteristics.
PID control is widely used in industry. Many experts and scholars have done a lot of research on PID control [
1,
2,
3,
4,
5]. P. R. ouyang et al. proposed a position domain nonlinear PD control method, which effectively improved the transient response performance [
1]. An online self-tuning PD controller of robot manipulators is designed in reference [
4]. It has good performance under large interference. With the development of science and technology, there are numerous nonlinear and intelligent control methods, such as backstepping control [
6,
7,
8], sliding mode control [
9,
10,
11], adaptive control [
12,
13,
14], robust control [
15,
16,
17],
control [
9,
18], fuzzy control, neural network control, feedback linearization control and so on. These control methods have aroused the interest of many scholars. Kanellakopoulos and Kokotovic et al. proposed backstepping control [
6]. Since then, backstepping control has been developed rapidly. Petit et al. adopted the backstepping control method of multi-joint robot tracking control to solve the problems of noise state measurement and high-order state derivative [
7]. However, the computational explosion problem of backstepping control is difficult to solve. Sliding mode control has fast dynamic response. It is insensitive to the system model and has high robustness. The single-loop sliding mode control of PMSM based on nonlinear disturbance observer is proposed in reference [
9]. In reference [
10], a new controller combining neural network with sliding mode control is proposed, which overcomes the requirement of system uncertainty bound by sliding mode controller. However, no matter how optimized, the chattering problem of sliding mode control still exists. It is inevitable that chattering damages the system. Adaptive control can adjust the parameters of the controller automatically. Sayed Bagher Fazeli Asl proposed an adaptive backstepping sliding mode control method, which improved the reaction speed of the system and effectively reduced chattering of the sliding mode [
11]. Han et al. taking robot tracking control as an example, adaptive method is adopted to improve the approximation performance of neural network [
13]. A new adaptive backstepping control method is proposed in the literature [
14], which improves position accuracy and has a good compensation effect for disturbance. However, the design of adaptive controller is very complex, and the stability of adaptive control is difficult to guarantee when the system uncertainty is large. Homayounzade et al. designed a robust controller for the robot system, which can deal with mechanical and electrical uncertainties at the same time, eliminating the limitations of previous robust control methods on system uncertainties [
15]. Makarov et al. used
framework to design a two-degree of freedom robot controller [
18], which cannot only withstand the uncertainty or change of model parameters, but also predict the future trajectory within a given time range and accurately track the given reference trajectory, with strong robustness. Fuzzy and neural network control have been widely concerned since they were proposed. However, due to the limitation of hardware, they are difficult to apply in practice. Feedback linearization control can adjust the dynamic response time of the system by assigning poles. Cambera et al. designed a feedback linearized controller [
19] by using double-loop cascade control to solve the trajectory tracking problem of single-link robot under the action of gravity. A simple learning strategy-based feedback linearization control for uncertain nonlinear systems is proposed in [
20]. Yin et al. designed a nonlinear state feedback controller for robots combined with energy shaping [
21], which can effectively suppress vibration and reduce motor position oversetting, and theoretically prove its global convergence.
All the above control methods are based on the idea of signal transformation. These methods can make the system have good dynamic response. In general, the steady-state characteristics of systems based on these methods are not very good. In 1989, Ortega and M. Pong proposed passivity-based control (PBC) to study the stability analysis and controller design of nonlinear systems [
22]. In 2002, professor R. Ortega et al proposed the passive control method of interconnection damping configuration (IDA-PBC) for the port Hamiltonian system [
23]. Professor Haisheng Yu applied Hamiltonian method to permanent-magnet synchronous motor and made good progress [
24,
25,
26]. PBC is based on the view of energy transformation and the research of PBC becomes very popular [
5,
27,
28,
29]. PBC can make the system have good steady-state performance, but its dynamic response is slow. A switching control method based on velocity error is proposed in reference [
30], but the chattering of SMC still exists.