Low frequency PID controller

This post is about how you can develop your own low frequency PID controller. Before I start giving out the details, let us refresh our knowledge about PID-

Theoretical Background for PID control

Whenever we want a system to reach a definite set point, we generate an error signal, which is a measure of how far our system is from the setpoint we want. usually it is in the form of a voltage. The most common example is that of a temperature controller. Usually the difference of resistance of the temperature sensor from that of the desired resistance, which is achieved when the desired temperature is reached, expressed in terms of the voltage gives the error signal. The PID controller generates a correctional signal, which drives the control unit of the system, with the correctional signal being a function of the error signal.

The output of the PID controller as a function of the error signal is given as follows-

As can be seen, the output voltage is proportional to not only the error signal but is also dependent on the 'history' of the signal as is given by the integral of the error signal and is also dependent on the rate of change of the error signal.

P, I and D controls how much will each of the terms affect the output voltage.

If we have only P, i.e., I and D are zero, then the system either oscillates about the setpoint which we are trying to achieve or never completely reaches the setpoint. The integral term kinds of dampens the oscillation about the setpoint while the differentiation terms increases the effect of dampening.

However, now definite theory of this process exists and though there are some established norms for determining the values of P , I and D for some specific systems, their choice is mostly made by trial and error, checking when the system responds in the most optimised manner.

Circuit for a low frequency PID control

By now most of the people who are familiar with electronic implementation of calculus, are thinking that this can be done using OP-AMPs, or operational amplifiers. It is true using standard Op-AMPs like 741 for low frequency operation. Below I am giving the circuit for the PID controller that I worked on for precision temperature control-

Multiple Op-Amps have been used other than the basic requirement of 4 so that we can maintain the frequency stability of the differentiator and integrator stages and also to maintain the required phase relationship between the error signal and the output voltage. The resistors which are equal are labeled as R and the variable resistors which are used are of 10K Ohm for the P stage and 1 M Ohm for the integrator and differentiator stages.

Design Hurdles

The main difficulty was faced during developing the integrator stage. It is the most unstable stage of the whole circuit and often showed a large offset voltage and low frequency modulation. It was removed by placing a high values resistor parallel to the feedback capacitance.

Another hurdle which was faced was due to impedance mismatch of the differentiator stage and adder stage. It lead to huge flyback for the D stage and was removed by using resistors for the adder stage comparable with that of the feedback resistance of the amplification section of the D stage,

Conclusion

All the ICs used was 741. This circuit is designed for very low frequency operation and was mainly tested for frequencies near 100 Hz. For high frequency operation, the integrator and the differentiator circuits have to be modified to compensate for bias stability of integrator and noise stability for the differntiator.