Type of controller (compensation network)

There are many types of compensation networks. They can be roughly divided into three types: lead, lag, and lag-lead. Applying them to compensate (or correct) the system is called lead correction, lag correction, and lag-lead correction, respectively.

(1) Lead compensation network. A compensation network with a lead phase is called a lead network. Applying lead network compensation can increase the bandwidth and phase margin, improve the transient response performance of the system, and reduce overshoot, but the high-frequency noise increases.

For example, the transfer function of the lead compensation network is

The network has a zero point of -1/T and a pole of -10/T. From the Bode plot analysis, it can be seen that the network has a leading phase and is a high-pass filter.

(2) Lag compensation network. A compensation network with a lagging phase is called a lag network. Applying lag network compensation can significantly improve the steady-state accuracy of the system, but slows down the transient response of the system.

For example, the transfer function of the hysteresis compensation network is

The network has a zero point of -1/T and a pole of -0.1/T. From the Bode plot analysis, it can be seen that the network has a lagging phase and is a low-pass filter.

(3) Lag-lead compensation network. It exhibits lag or lead network characteristics in different frequency bands. Using lag-lead network compensation not only improves the steady-state accuracy of the system, but also improves the transient performance.

For example, the transfer function of a lag-lead compensation network is

The network has two poles at -10/T and -0.01/T, and two zeros at -1/T and -0.1/T. It has the characteristics of a lagging network in the low frequency band and the characteristics of an advanced network in the high frequency band. In the low frequency band (<0.01/T) and high frequency band (>10/T), the gain is 0dB.