1. Project 4: Emulating Human Reasoning Through Enhanced Decision Making
Team Members:
Adam Katterheinrich (Aerospace Engineering - Junior)
Nicholas Nielsen (Aerospace Engineering - Junior)
Tyler Parcell (Computer Engineering - Sophomore)
AC: Dr. Kelly Cohen
SAC: Dr. Jeff Kastner
GRA: Mr. Wei Wei

2. Project Introduction

3. Real World Application
Provides a foundation for autonomous control
Allows integration of “Human Reasoning” into control systems
NAE Grand Challenge
“Reverse Engineering the Brain”
Highly useful for firefighting, aerial photography, package deliveries, hobbyists, etc…
Introduction

4. Project Overview and Goals
A dynamic Quadrotor model has been previously developed
Goal is to control the model using Fuzzy Logic techniques
The well known inverted pendulum model will be utilized as a benchmark problem to prove the abilities of the Fuzzy controller
Use Fuzzy PID for pendulum as starting point for quad- rotor control/stabilization
Introduction

5. Fuzzy Logic Controller
What is Fuzzy Logic?
Based on "vagueness" in the real world
Streamlines Design process with linguistic variables
More possible solutions than conventional logic
“Human Reasoning” integrated into system
Fuzzy Logic Controller
Fuzzification
Fuzzy Rule Base
Inference
Defuzzification
Crisp Input Data
Crisp Output Data
Introduction

6. Experimental Methods

7. Inverted Pendulum Control
Pendulum is balanced on a cart
Created simulation using MATLAB’s Simulink
Based on equations of motion
𝐼+ 𝑚𝑙 2 𝜃 +𝑚𝑔𝑙 sin 𝜃 =−𝑚𝑙 𝑥 cos 𝜃
𝑀+𝑚 𝑥 +𝑏 𝑥 +𝑚𝑙 𝜃 cos 𝜃 −𝑚𝑙 𝜃 2 sin 𝜃 =𝐹
PID controller
Fuzzy PID controller
Controller
Experimental Methods

8. Quad-Copter Control Utilize previously developed model
Input signals provided using real flight data
Stabilization on a single axis using a PID controller
Angle and Angular Velocity evaluated
Dual Fuzzy PID controller based on Pendulum controller
Single Fuzzy PID controller
Experimental Methods

9. What is a PID Controller?
PID is short for Proportional, Integral, and Derivative
Proportional: Produces quick responses by multiplying the feedback (current error in the system) by a scaled constant.
Integral: Eliminates steady state errors by combining past errors and compensating or accelerating the response to make up for the accumulation over time
Derivative: Calculates the future behavior of the system based on the slope of the response
Experimental Methods

10. Why Fuzzy PID? Dynamic modification of gains
Allows for rule-based control
Adaptable to small system changes
Expanded Performance Envelope
Experimental Methods

11. Fuzzy Architecture - Input
Experimental Methods

12. Fuzzy Architecture - Output
Experimental Methods

13. Experimental Results

14. Constraints 50 second simulation time Half degree Angle deviation
Half meter Position deviation
Signal limited to ±5N force
Stabilization Definition:
The time it takes to get within the determined bounds and stay within those bounds (for 20% of simulation time)
Tests utilizing random sensory and force noise
Experimental Results

15. PID Performance Envelope
Experimental Results

16. Fuzzy PID Performance Envelope
Experimental Results

17. PID Performance Envelope with Sensory Noise
Experimental Results

18. Fuzzy PID Performance Envelope with Sensory Noise
Experimental Results

19. PID Performance Envelope with Force Noise
Experimental Results

20. Fuzzy PID Performance Envelope with Force Noise
Experimental Results

21. Fuzzy PID compared to PID Fuzzy PID compared to PID
PID vs. Fuzzy PID
Performance Envelope
No Noise
Sensory Noise
Force Noise
PID
204 pts
172 pts
232 pts
Fuzzy PID
312 pts
274 pts
334 pts
Fuzzy PID compared to PID
+53%
+59%
+44%
Settling Time
No Noise
Sensory Noise
Force Noise
Average change in settling time with Noise
PID
2.91 s
8.07 s
3.08 s
2.66 s
Fuzzy PID
4.79 s
4.82 s
4.81 s
0.03 s
Fuzzy PID compared to PID
+64%
-40%
+56%
Experimental Results

22. What happens if Fuzzy Logic is applied in conjunction with the conventional PID?
Positives
Negatives
Active gain updating which results in better force responses at large deviations to keep the pendulum stable
Robust performance envelope for angle and cart position anomalies
Consistent behavior to sensory noise and outside force inputs
More computationally intensive because of the entire PID system working in conjunction with the fuzzy calculations
Slightly longer average settling time
Experimental Results

23. Dynamic Quad-rotor Model24
Dynamic Quad-rotor Model
Experimental Results

24. Dynamic Quad-rotor Model25
Dynamic Quad-rotor Model
Experimental Results

25. Conclusion
Standard PID Controller provides a good benchmark for Fuzzy Logic Controller
Created a Fuzzy PID Controller
Performance Envelopes show that Fuzzy PID is more robust, but has a trade off of settling time (sometimes)
Fuzzy PID Controller can easily be adapted to Quad-rotor control/stabilization

26. Project Timeline Tasks Week 1 Week 2 Week 3 Week 4 Week 5 Week 6
Fuzzy logic Training
Flight simulator training
Literature and mathematics review
Building pendulum model
Develop Fuzzy logic controller for the pendulum model
Develop Fuzzy logic controller for quad-rotor aircraft using pendulum controller as a blueprint
Controller Testing on simulated Quad-rotor
Final Report preparation
Final Presentation

27. Questions?
Araki, M. (2006). PID Control in Control Systems, Robotics and Automation, vol II. In Encyclopedia of Life Support Systems (EOLSS).
Bih, J. (2006). Paradigm shift - An introduction of fuzzy logic. Potentials, IEEE, 25(1), 6-21.
Mendel, J. (1995, Mar). Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE, 83(3),
Michigan, R. o. (Ed.). (96, 8 30). Modeling of an Inverted Pendulum. Retrieved 6 19, 2014, from Control Tutorials for Matlab:
Razzaghi, K. (2011, 11 01). A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller. Advanced materials research, pp
References
Special thanks to the National Science Foundation
for sponsoring this research project:
Grant ID No.: DUE