Sysquake Pro – Table of Contents

Sysquake – Table of Contents

Sysquake for LaTeX – Table of Contents

PID_dt.sq

Discrete-time PID controller

The PID controller is fundamentally a continuous-time controller. However, it is often implemented with digital electronic devices (such as microcomputers, microcontrollers, or FPGA). Sampling effects may change performance in subtle ways, especially when the sampling frequency is not very high with respect to the bandwidth of the controlled system. Instead of converting a continuous-time PID controller, it is possible to design a PID directly in the discrete-time domain, approximating the integration and derivation by sums and differences, respectively. The parameters of the PID keep their standard meaning. PID_dt.sq does for discrete-time PID controllers what PID_ct.sq does for continuous-time PID controllers. In its simplest form, the transfer function K(z) of the PID is

where Ts is the sampling period.

Like the continuous-time PID controller, the discrete-time controller is usually not implemented like this: the derivative term is not applied to the set-point, the proportional gain is reduced for the set-point, and the derivative action is filtered. The transfer function used for feedback is

Figures

The figures are the same as those defined for RST_dt.sq, except for the Open-Loop Zeros and Poles and the Closed-Loop Poles which are not defined.

Settings

The System (continuous-time model), System (discrete-time model), Sampling Period, and Damping Specification have the same effect as the corresponding menu entries defined in RST_dt.sq. Two new entries are defined.

PID Coefficients

The three parameters of the PID (kp, Ti and ) can be edited in a dialog box. For P, PI, or PD controllers, set the parameter of the missing component to the empty matrix [].

No Derivator On Reference

When the input of the PID controller is the error between the set-point and the measured output, discontinuities of the set-point are differentiated by the derivator component of the PID and yield infinite values (or very large values in the case of a discrete-time PID controller) for the control signal. To avoid that, the set-point is usually not differentiated. The control signal is

Display Frequency Line

When selected, moving the mouse above a frequency response (Bode or sensitivity) will display a corresponding line in other frequency responses, Nyquist diagrams, and zero/pole diagrams.