Mathematical modelling and analysis of electromagnetic-ball-suspension control system.

This dissertation presents some of the mathematical approaches that deal with Control Theory. Emphasis is put on modelling and analysis of EMBSS. Jayawant (1982) modelled the EMBSS with RLC circuit. However, he described that the problem which arises is; once the circuit is disturbed the ball always diverges oscillations. In his model he did not take into account of the effect of the air resistance. SUN (2010) studied the EMBSS and found that it has disadvantages of heat generation, high power, low potential, and the use of a big size of the coil. It is difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. To address these issues we extend two models, model one: when the input of the system is designed to be the voltage and model two: when the input of the system is designed to be the current. The ranks of two special matrices; the controllability matrix and the observability matrix are used to check if the above-mentioned systems are controllable or observable. The study also deals with the feedback linearisation which helps in linearising completely the two models of EMBSS. Optimal control is applied so that the required input can be chosen for the desired output of the EMBSS; which is the desired position of the ball from the lower end of the electromagnet. The results show that the EMBSS is both controllable and observable. Stability is guaranteed under certain conditions. The EMBSS is feedback linearisable and optimal control was performed adequately on both linearised models.