Lesson Summary

PID Control

Water Level PID Control

Using the same training kit at the same control cycle time for Fuzzy control, water tank level control of first order lag is realized by PID control.

PID Control Equation

MV=(100/Pb)((1/1+Tis)×e-(Tds/(1+0.1Tds))×PV)

MV : Manipulated Variable 100/Pb : Proportional Gain e : SV-PV SV : Set Value

s : Laplace Operator Pb : Proportional Band Ti : Integral Time Td : Derivative Time PV : Present Value

In PID control, the respective effect given by each parameter of Pb, Ti and Td can be easily understood since those three outputs are separately computed and displayed in graphics. However, the actual control output is a sum of those output.

PID Control Display Window

Upon mouse-clicking the "Control Display" in the menu, the Control-display window opens. The above window shows the stabilized water level status at the target level after controlling it actually. Since the time axis is common to that for Fuzzy control, you can check the difference of the control effect between PID and Fuzzy controls. In the above window, you can see that each output from the proportional, integral and derivative controls is displayed respectively.

Fuzzy Control

Water Level Fuzzy Control

As illustrated above, water tank level control of first order lag is realized by Fuzzy control. The water control tank is provided with a hole so that the water always flow out at a speed in proportion to its water level. To keep the water level at the set value, the pump must be always operated under a proper control. In Fuzzy control, such pump operation is realized using a combination of the position-type control (rough tuning) where the manipulated variable is determined by the deviation of the present value from the set value and the speed-type control (fine tuning) where the offset from the set value is adjusted.

Control Operation Block Diagram

The hardware configuration to make it commonly applicable to PID control is shown above. For Fuzzy inputs, the software is designed to enable such assignments as the "level deviation" at Ant-1, "level change" at Ant-2, "set value" at ant-3 and "set change" at Ant-4. While such assignments as the position-type control output at Cnsq-1 and speed-type control output at Cnsq-2 are enabled by the software as well as their sum are used as the control output.

Fuzzy Rule Explanation

Rough Tuning

The rules No. 1 - 3 are used to determine the position-type control output in response to only the input of the water level deviation. The input of the water level change is ignored for the rough tuning.

Fine Tuning

When the water level deviation does not become zero as a result of the control output from the rules No. 1 - 3 or due to the pump capacity fluctuation, the disturbance, etc., the rules 5 and 6 are used to determine the speed-type control output for fine tuning in addition to the above position-type control output.

Fuzzy Control Display Window

Upon mouse-clicking the "Control Display" in the menu, the Control-display window opens. The above window shows the stabilized water level status at the target level after controlling it actually. Fuzzy control has a shorter convergence time than PID control and can be realized using only 5 rules. It is a great feature of Fuzzy control where the human rules of thumb can provide the nonlinear outputs in response to the water level deviation data in different from PID control where all the proportional, integral and derivative controls can provide the only linear outputs.

 (C) 2004 ADWIN Corp.