Design of the PWM-PID controller

The rise and fall time of the modulated pulse width, T , depends on that of the driving circuit loaded by the actuator capacitance. The time 

Ta also affects the width (Ton) of the output square pulse s t). Ton is calculated as follows [Zhao and Jones (1997)]  

When Ton 0, we assumed that Ton = 0. Consequently, the rise and fall time of the driving circuit, Ta, should be minimized. Ad represents the amplitude of the modulated signal at ON state. 

Based on the PW modulator, the PID controller is designed to control the multi-stacked actuator. The control system is illustrated in Fig. 7.24. The PID controller transforms the error between the command and the feedback signals from the sensor to the command for the PW modulator. The PW modulator transforms the output of the PID controller into a pulse sequence, which is applied to the multi-stacked actuator. 

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