Given a plant with a transfer function of K/s, how can I tune a PID to control it? I found articles explaining how to tune an integrator with time delay, but not for just a pure integrator system.
Ideal Water Tank
Figure. Closed-loop water level control system
Figure 3 can be used as mentioned in comment above :
T(s) = 1 / ( A * s ) where Flow = Area * ( dHeight / dTime )
If all parameters set (positively), this system will be stable also. Changing controller parameters will change the response of system but not the stability.
- MATLAB Simulink can be also used in the design process.
Selecting Controller Parameters
One can choose different controller parameters for K1, K2*s, K3/s terms. This will only change the general response behaviour of system but this will not change the stability of system, so it will remain stable.
There are multiple ways to select them;
- Inspect the Previous Applications
- Inspect the Articles about the subject if unique
In the design process, one must consider the requirements of the system. Also in some preferred programs like MATLAB can be useful with Simulink in the design process. There are number of common terms in transient response characteristics and which are;
- Delay time (td) is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.
- Rise time (tr) is the time required to reach at final value by a under damped time response signal during its first cycle of oscillation. If the signal is over damped, then rise time is counted as the time required by the response to rise from 10% to 90% of its final value.
- Peak time (tp) is simply the time required by response to reach its first peak i.e. the peak of first cycle of oscillation, or first overshoot.
- Maximum overshoot (Mp) is straight way difference between the magnitude of the highest peak of time response and magnitude of its steady state. Maximum overshoot is expressed in term of percentage of steady-state value of the response. As the first peak of response is normally maximum in magnitude, maximum overshoot is simply normalized difference between first peak and steady-state value of a response.
The controller parameters so the characteristics of the system must satisfy the system requirements. There are more formulas about each of them depending on the systems characteristic equation's order etc. While changing parameters, it will be useful to simulate the response to visualize the problem.