When designing control loops, we often encounter non-linear systems that have much more complex dynamics than linear systems. This means that we cannot use classical control algorithms to guarantee that the control loop works sufficiently well over the entire operating range. Therefore, in this master thesis we focus on the control of a nonlinear dynamic system with more advanced nonlinear controllers. All experiments were performed on a semi-helicopter laboratory device. The device consists of a pendulum which is rotatably mounted in the center. On the left side of the pendulum is a counterweight and on the right side is an electric motor with a propeller. The system receives the voltage at the electric motor as input and returns the offset angle as the output. The device shows non-linear operation and a rather oscillating response, so it is particularly suitable for testing developed non-linear controllers.
The entire master's thesis is divided into six main chapters. In the first introductory chapter, we briefly present the theoretical foundations of the control of dynamical systems. Since we will encounter more advanced nonlinear controllers based on a nonlinear system model, we briefly introduced the theory of identification of the nonlinear system model.
As mentioned earlier, we will use more advanced approaches to control our system. Therefore, in the second chapter we have presented the theory in more detail and derived the expressions of all the advanced controllers used. In the master thesis we have used three different controllers: Fuzzy Predictive Function Controller (FPFC), NARMA L2 Neural Network Controller and PID controller with optimised parameters.
All experiments were conducted on a semi-helicopter laboratory device and its mathematical model, so that the fourth chapter of the master's thesis is devoted to the analysis of the static and dynamic properties of the laboratory device. It has been found that a good knowledge of the properties of the system is crucial for the successful design of experiments and control algorithms. We first developed all the control algorithms on the model of the device, as it is much faster to collect measurements and identify the model, and it is also much easier to look for errors in the program code. Then we developed the controls on the real system and observed what changes we had to make to make a more complex control work successfully on the real system.
After the analysis of the laboratory device and its model, in the fourth chapter we present the results of control with developed regulators.
We first present the results for each controller, which we compare in the last subsection of chapter four to determine the best controller type for our problem. It turns out that the best control results are obtained with an FPFC controller, but the development of the FPFC is more time-consuming than that of a PID controller. The PID controller works well at the beginning of the working range (smaller offset angles of the helicopter), but at higher offsets the system response becomes quite oscillatory. The FPFC has much less oscillation than the PID controller, but at steady state it performs worse than the PID controller at removing disturbances. The NARMA L2 controller works quite well when run on a system model, but we were not able to train the controller on a real system. When we run the NARMA L2 controller on a real system, we get an unstable system response and we never manage to get good performance.
Chapters five and six are followed by an even more detailed discussion of the results and the conclusion of the master's thesis.
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