A fuzzy PD controller is a proportional-derivative controller. But in this case, it is better called as Present Error-Derivative of Present Error. It uses fuzzy logic software principles as a form of error control in industrial systems. PD controllers are widely used in automation to adjust valves and other process controls based on the accumulation of errors over time. Where a fuzzy PD controller differs from a standard PD controller is in its ability to provide more accurate results in nonlinear situations. Fuzzy systems are built on a type of programming logic that tries to deal with gray areas of process uncertainty more successfully than standard controls.
One of the problems with a fuzzy PD controller is that it can arrive at conclusions that are mutually contradictory and take no action. This requires a process of conflict resolution in the code that is commonly referred to in fuzzy systems as defuzzification. Defuzzification is done by giving certain parameters in a PD controller greater weight than others to tip the balance in a certain direction of action, and this is analogous to an adjusted gain in a standard PD controller.
The advantages that a fuzzy PD controller offers include that it can provide different response levels to non-linear variations in a system, and, at the same time, it can function as well as a standard PD controller in a system where variation is predictable. A fuzzy PD controller can also keep a system more stable. It can be weighted towards types of responses just like the gain settings on a standard PD controlled system as well.
For this project, the ranges of arm positions were previously defined, which are:
| Name | Range of Positions |
|---|---|
| Side Shoulder | 0.07 <= dA[0] <= 2.68 |
| Vertical Shoulder | -1.5 <= dA[1] <= 1.02 |
| Upper Arm | -3.46 <= dA[2] <= 1.5 |
| Elbow of the Arm | -0.32 <= dA[3] <= 2.29 |
| LowerArm | -2.07 <= dA[4] <= 2.07 |
| Doll of the Arm | -1.39 <= dA[5] <= 1.39 |
| Wrist Rotor | -2.07 <= dA[6] <= 2.07 |
The speed ranges required to move the arm to a desired position were also defined:
| Name | Range of Speed |
|---|---|
| Side Shoulder | -1.95 <= vA[0] <= 1.95 |
| Vertical Shoulder | -1.95 <= vA[1] <= 1.95 |
| Upper Arm | -2.35 <= vA[2] <= 2.35 |
| Elbow of the Arm | -2.35 <= vA[3] <= 2.35 |
| LowerArm | -1.95 <= vA[4] <= 1.95 |
| Doll of the Arm | -1.76 <= vA[5] <= 1.76 |
| Wrist Rotor | -1.76 <= vA[5] <= 1.76 |
Diagrams of the seven fuzzy PD controller.
In this project, Webots R2019b was used with a pre-designed robot called TIATGo_AP2_CD. The folders are structured as follows:
📂 Controllers
Control_Steel.java --> Main Class.
Agente_Difuso.java --> Here the fuzzy controller is done.
📂 Info
CDataTIAGo-Steel.txt --> Relevant info on position ranges and speeds.
📂 Protos
Supporting information for the simulation.
📂 Worlds
The simulation.
The definition of present errors is this:
1.1.
- Present Error of Side Shoulder (Desired value - Sensed value)
- T(X1): BN/SN/Z/SP/BP
| ACRONYM | Name |
|---|---|
| BN | Big Negative |
| SN | Small Negative |
| Z | Zero |
| SP | Small Positive |
| BP | Big Positive |
- U1: [-2.61;2.61]
1.2.
- Derived from the present error of Side Shoulder (Present Error - Past Error)
- ΔT(X1): BN/SN/Z/SP/BP
- ΔU1: [-5.22;5.22]
2.1.
- Present Error of Vertical shoulder.
- T(X2): BN/SN/Z/SP/BP
- U1: [-2.52;2.52]
2.2.
- Derived from the present error of Vertical shoulder.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-5.04;5.04]
3.1.
- Present Error of Upper Arm.
- T(X2): BN/SN/Z/SP/BP
- U1: [-4.96;4.96]
3.2.
- Derived from the present error of Upper Arm.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-9.92;9.92]
4.1.
- Present Error of Elbow of the Arm.
- T(X2): BN/SN/Z/SP/BP
- U1: [-2.61;2.61]
4.2.
- Derived from the present error of Elbow of the Arm.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-5.22;5.22]
5.1.
- Present Error of Lower Arm.
- T(X2): BN/SN/Z/SP/BP
- U1: [-4.14;4.14]
5.2.
- Derived from the present error of Lower Arm.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-8.28;8.28]
6.1.
- Present Error of Doll of the Arm.
- T(X2): BN/SN/Z/SP/BP
- U1: [-2.78;2.78]
6.2.
- Derived from the present error of Doll of the Arm.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-5.56;5.56]
7.1.
- Present Error of Wrist Rotor.
- T(X2): BN/SN/Z/SP/BP
- U1: [-4.14;4.14]
7.2.
- Derived from the present error of Wrist Rotor.
- ΔT(X2): BN/SN/Z/SP/BP
- ΔU2: [-8.28;8.28]
The matrix of centers is as follows:
private double[][][] MatrizDeCentros = { { {-0.4875,-0.975,-0.975,0.975,0.4875},
{-0.975,-1.4625,-0.4875,1.4625,0.975},
{-1.95,-0.975,0,0.975,1.95},
{-0.975,-1.4625,0.4875,1.4625,0.975},
{-0.4875,-0.975,0.975,0.975,0.4875}},
{ {-0.4875,-0.975,-0.975,0.975,0.4875},
{-0.975,-1.4625,-0.4875,1.4625,0.975},
{-1.95,-0.975,0,0.975,1.95},
{-0.975,-1.4625,0.4875,1.4625,0.975},
{-0.4875,-0.975,0.975,0.975,0.4875}},
{ {-0.5875,-1.175,-1.175,1.175,0.5875},
{-1.175,-1.765,-0.5875,1.765,1.175},
{-2.35,-1.175,0,1.175,2.35},
{-1.175,-1.765,0.5875,1.765,1.175},
{-0.5875,-1.175,1.175,1.175,0.5875}},
{ {-0.5875,-1.175,-1.175,1.175,0.5875},
{-1.175,-1.765,-0.5875,1.765,1.175},
{-2.35,-1.175,0,1.175,2.35},
{-1.175,-1.765,0.5875,1.765,1.175},
{-0.5875,-1.175,1.175,1.175,0.5875}},
{ {-0.4875,-0.975,-0.975,0.975,0.4875},
{-0.975,-1.4625,-0.4875,1.4625,0.975},
{-1.95,-0.975,0,0.975,1.95},
{-0.975,-1.4625,0.4875,1.4625,0.975},
{-0.4875,-0.975,0.975,0.975,0.4875}},
{ {-0.44,-0.88,-0.88,0.88,0.44},
{-0.88,-1.32,-0.44,1.32,0.88},
{-1.76,-0.88,0,0.88,1.76},
{-0.88,-1.32,0.44,1.32,0.88},
{-0.44,-0.88,0.88,0.88,0.44}},
{ {-0.44,-0.88,-0.88,0.88,0.44},
{-0.88,-1.32,-0.44, 1.32,0.88},
{-1.76,-0.88,0,0.88, 1.76},
{-0.88,-1.32,0.44,1.32,0.88},
{-0.44,-0.88,0.88,0.88,0.44}}};Finally, a total stabilization in 10 seconds was obtained as a result.
Final result applied in Webots.
Please feel free to use it if you are interested in fixing issues and contributing directly to the code base.
Backpropagation is released under the MIT license. See the LICENSE file for details.