Theory: In most of the feedback control engineering systems, the speed of achieving stable response for a given input (set point) is the criteria for proper control. Often in any control system, the actuating elements namely motors, tacho-generators etc are all inherently inertial system with finite damping, the system response for stability can be achieved by adding compensating network, so that they react faster to achieve stability than without these compensators. The most important part of the feedback loop for the designer is the loop filter. It is basically a low-pass filter with a corner frequency that should be well below the signal frequencies, so that the control voltage to the system is relatively steady. However, the system must be able to respond to changes, so the corner frequency should be above the frequency of those changes. Quite often, we want a system that responds rather slowly, to provide a flywheel action that damps out noise and unwanted variations. It is a delicate matter of compromise, and the designer's tool is the loop filter. Therefore there exists a need to understand what these LEAD-LAG Network is all about. The simplest and really, satisfactory loop filter is the so-called lead-lag filter. It is an RC low-pass filter with an extra resistance in series with the capacitor. The pole provides a phase lead, while the zero a phase lag, so that the phase is zero both at low and high frequencies. It is easy to draw a Bode plot of the phase variation, as well as of the gain. One method of loop filter design is to determine satisfactory values for fc and f2, and then to proportion the filter reasonably. The resistors can be larger if the capacitor is smaller, and vice-versa. About LEAD-LAG Network trainer: In this LEAD-LAG network trainer, it is possible to study the following transfer functions, with the help of an external function generator and dual beam Oscilloscope. 1. for Lead- Lag transfer function
1 +sT2 / 1+a T1
2. for a Integrator and Lead transfer function of
1 +sT2 / sT1
3. for a Integrator and Lead with phase compensator transfer function of
(1 / sT1) (1 +sT2 / 1 +sT3) By proper adjustment of the input signal source, it is possible to observe the corner frequencies. In order to accomplish the above, the trainer has all the necessary components, Op-Amp, built-in power supplies. Interconnections between the devices are by using patch cords. At the end it is necessary to draw the Bode plot for analysis. An external function generator operating in the range of 100Hz to 10KHz is required as signal source. A dual beam oscilloscope is required to observe the input output waveforms. At low frequencies, it is necessary to have a storage oscilloscope to record slow varying input signals. Optional: When this Study of Lead and Lag Network Model LLN-1 is connected to PID trainer Model PID-2 and Speed Control of DC Motor using Chopper Drives Model PE-10, it forms an excellent full fledge laboratory tool. Because PID-2 is a PC based system, with plenty of post analysis capability. In this way one can observe the real physical system, responding to the actual plant situations. |
