Popular romance of UAV flight control

Although control as a discipline has only developed for a hundred years, people have already started to use feedback in real life. In ancient times, there was a kind of timing tool-"Copper Pot Drip". The ancient book records that "the leaky work was made on the day of Xuanyuan, and it was proclaimed as the generation of Xia and Shang Dynasties", indicating that the application of drip timing was very long. The original drip timing equipment only had a leaky kettle. With the passage of time, the water level in the kettle dropped, thus driving the ruler floating in the water to drop to indicate the elapsed time. However, because the water level in the leaky kettle is changing, the rate of water leakage is also changing, which makes the timing inaccurate. The ancients must have discovered this defect and constantly improved it. The most famous copper kettle drip casting and Yuan Dynasty consists of four kettles, the bottom of which is the receiving kettle, in which a ruler floating in the water is placed to show the time, while the setting of the above three day, month and star kettles is to keep the water level of the last leaky kettle constant, so as to obtain a constant water leakage rate. However, this design needs to ensure that the dripping speed of the moon kettle is always faster than that of the Xinghu Lake. The ancient Greek craftsman Ketcibius designed a more exquisite mechanism. Although the design only has a three-stage kettle, a special float is placed in the middle kettle. When the water level reaches a certain height, the float will block the outlet of the superior kettle. In this design, the basic idea of negative feedback was used and it became the earliest liquid level controller in human history.

Feedback is very important to control, and it can even be said that control has really become a technology since people consciously use feedback to solve engineering problems. People have also invented various automatic control devices in their production and life, and the steam engine governor invented by Watt is one of the most famous devices. The governor uses the principle of centrifugal governor used in windmills in the early days, and the rotating shaft of the governor is fixedly connected with the rotating shaft of the steam engine. When the speed of the steam engine is too fast, the height of the metal ball of the governor increases, reducing the opening of the air inlet valve, thereby reducing the speed of the steam engine; When the speed of the steam engine is too slow, the governor will increase the opening of the intake valve.

If the development of control as a technology stops here, there will be no problem with the assertion that "control is to increase the size and decrease the size" at the beginning of this paper. As long as the artificial system can spontaneously increase the size and decrease the size, it can be considered as an automatic control system with feedback. But in fact, the development of control science has just begun.

The steam engine governor is important for one thing, because with the large-scale use of steam engines, the popularity of the device is also very high, and another reason is that the operation of the device also involves one of the essences of control science-stability. At the beginning of the governor's use, the operation effect was very good, but when the speed of the steam engine was greatly improved, some governors began to fail to operate stably. This problem could not be solved under the theoretical and technical conditions at that time. After studying this unstable problem in depth, the British physicist Maxwell described the working principle of the governor by using differential equations and linearized the differential equations at the equilibrium point. Furthermore, it is found that this system can run stably only when the roots of the characteristic equation all have negative real parts. With the deepening of research, routh criterion, Hurwitz criterion, Nyquist criterion and Lyapunov stability criterion have been put forward one after another. It is after people began to study the stability of the system that control officially became a science. At this time, control has become "big and small, small and big" on the premise of ensuring the stability of the system.