Flexible Broom Balancing

Ashab Mirza

Iram Mahboob

MS (Aerospace Engineering), France.

Member IEEE, Inc., USA

Ph.D. Student of National University of Sciences & Technology (NUST) at PNEC, Karachi.

Supervisor: Dr. Sarfraz Hussain, Dean (EPE), NUST at PNEC.

BE (Industrial Electronics),

Student Member IEEE, Inc., USA

MSEE. Student of NUST at UNSW, Australia.

One should not be a control engineer to realize that an inverted broomstick pivoted at bottom is bound to go down by even a slightest disturbance. This problem becomes more difficult when the broom is pivoted on a cart (or trolley) and the broom is to be stabilized by its linear motion. The degree of complexity is further aggravated if the broomstick is flexible. That is why, this problem is of great interest to Control Engineering students and researchers. Different approaches have been tried to give a suitable solution to the problem. While going through print material on the subject, it was found that the researchers and experts had reservations about effectiveness of the solution to the problem that would be based on classical or linear control theory. In this paper this aspect is thoroughly investigated and a novel solution to this problem is presented. That is:

A law for estimation of the gains of the PID controller, and full solution to a rigid-body broom balancing problem.

Mathematical Modeling technique for a flexible structure, Analysis of the problem of bending oscillations caused by the flexibility, Discussion on the different solutions to the problem, and finally Experimental Results, Analysis & Comparison Hardware implementation and practical results of the designed control loop. And, Comparison of Practical and Simulated results of the solution.

These solutions are directly applicable in aerospace industry, for, the dynamics of a flexible broom is comparable to the dynamics of pitching (or yawing) of a long (flexible) rocket, e.g., a satellite launch vehicle. By a very crude relationship, a rocket whose length to diameter (L/D) is greater then ten (10), poses considerable bending oscillation that cannot be ignored. Several times launch vehicle went uncontrolled and met a disaster just after their liftoff, only because, while designing its control loop, the control system designers failed to consider the its bending oscillations due to flexibility in the mechanical structure.