2.2.3. Stribeck Friction Model

Because the frictional disturbance torque in the EMA system has a high degree of nonlinearity and complexity, it has a greater impact on the control performance of the system, causing the system to crawl at low speeds, and there will be larger errors in the steady−state. The Strobeck friction model is the most common friction model in engineering, which can fully and accurately reflect the friction phenomenon in the EMA system. The expression of the disturbance torque is [32]

where, T_f is the friction torque of the system, T_l is the Coulomb friction torque, T_s is the maximum static friction torque, ω is the angular velocity of the motor output shaft, ω_s is the Stribeck speed, and b is the viscous friction coefficient.

Generally, friction models are divided into continuous and discontinuous models. The main difference is whether it is continuous at zero speed [33]. The Stribeck friction model used in this article is a discontinuous model, so it has the problem of speed zero crossing detection. In the Stribeck friction model, a symbolic function is used. Since the generalized zero velocity is difficult to measure, the saturation function is used instead of the sign function to solve the problem of velocity zero crossing detection.2.2.3 EMA system model.

According to the above analysis of each part of the EMA system, according to the working principle of the EMA system, when the external load is 0, the open−loop transfer function of the EMA system can be obtained as

According to the above analysis and the open−loop transfer function of the system, the overall control block diagram of the system can be obtained, as shown in Figure 2.

Block diagram of the open-loop transfer function of the EMA system.

In Figure 2, T_L is the sum of frictional disturbance torque equivalent and other load disturbances to the motor output shaft.