Software-based adjusting P-I gain controller for speed-tracking servo system using traveling-wave type ultrasonic motor

Neuro-fuzzy speed tracking control of traveling-wave ultrasonic motor drives using direct pulsewidth modulation

“…By adopting the center-of-area defuzzification method [18], the defuzzified output is given by (10) where is the input of the th term of the th output linguistic variable, while and are the corresponding mean and variance of the bell-shaped membership function, respectively. Hence, it yields (11) (12) Thus, the layer-5 link weight is . In this application, the bell-shaped characteristic functions are used to describe the output linguistic variables and .…”

“…into (13), can be obtained as (17) By using (11) and (12), can be obtained as (18) Hence, by substituting (17) and (18) into (15), and then using (14), is updated by (19) Similarly, by using (11), (12), (14), (16), and (17), is updated by (20)…”

“…By using (17), the error to be propagated to layer 4 is given by By using (11) and (12), can be obtained. Hence, making use of (21), (23) can be expressed as (24) Similarly to layer 4, there is no weight to be adjusted in layer 3.…”

“…Many published papers concerning motion control of the TWUM adopt a general servo control system for hardware implementation [12]- [17]. This system generally employs a microcomputer which commands a dual-channel function generator to provide proper switching signals for the two-phase inverter [4].…”

“…Although many attempts have been made to model the TWUM, the resulting models are so complex or data demanding that they are impractical for real-time control [9]- [11]. Alternatively, many empirical approaches, such as proportional integral (PI) control [12], fuzzy logic control [13], adaptive control [14], and neural network control [15], have been proposed for motion control of the TWUM. The PI control is simple and offers a wide stability margin.…”