Question

When trying to implement PID control, it is said that we typically find three types of processes, namely:

a) Resistance Type Processes

b) Capacitance Type Processes,

c) Inertia Type Processes. In most instances, Inertia processes are quite uncommon. Carefully consider your experience over the years, and describe an application, which according to your understanding of the subject matter, comprises of both Resistance and Capacitance effects.

Answer 1

In a level controller system the level of the water And the tank is kept constant while on the other hand drawing water from the tank. To keep the level of the water constant one should keep the input flow rate of the water matched with output flow rate in the tank.

the model tells us how H will change if we adjust Q1 in flow while we keep the outflow Q2 constant setting.

The model equation isdH/dt =Q1-Q2/A & Q2=H/R

the first equation says the rate of change of level is proportional to the difference between inflow and outflow divided by the cross sectional area of the tank. The second equation says the outflow will increase in proportional to pressure head divided by the flow resistance R.

The process input/ output relationship is therefore obtained by substituting Q2 in linear differential equation dH/dt =Q1/A - H/RA

which is rearrange to standard form

RA dH/dt + H = RQ1

after solving for H we get

H = RQ1(1-e^ - t/RA)

using this equation we can show that if a step change in floor Delta Q1 is applied to the system the level will rise by an amount Delta Q 1 R by following and exponential rise versus time.

This is the characteristic of first order dynamic process and is very commonly seen in many physical processes. These are sometimes called capacitive and resistive process and include charging of capacitor through resistive circuit.