Στη παρούσα διπλωματική μοντελοποιείται το σύστημα σφαίρας ράβδου. Εξάγεται το μοντέλο στο χώρο κατάστασης και υλοποιείται γραμμικοποίηση εισόδου κατάστασης και εισόδου εξόδου. Βρίσκονται προσεγγιστικοί νόμοι ελέγχου για το μη γραμμικό σύστημακαθώς παρουσιάζει ιδιομορφία. / This diploma thesis includes the analysis of the nonlinear system of a ball-beam and the design of different control laws. Initially, we present the physical system and we derive the mathematical model from the lagrange equation.The nonlinear system fails to be stable with the classic linear control laws and we try to stabilize it by input-state and inputoutput linearization. The ball beam system fails to be controlled by full state linearization and we proposed some approximations for inputoutput linearization. We describe in detail how we can derive the approximate control laws and through simulation we are capable of choosing the best suitable control law. We propose a switch-controller for the nonlinear system which is vital for systems with undefined relative degree and are not input state linearizable.