Robust control of unstable systems: algebraic approach using sensitivity functions

This contribution proposes a methodology for robust control of unstable systems. For this purpose the algebraic approach using polynomials is utilized together with tuning some of the closed loop poles using loop sensitivity functions. The control design method is illustrated on the stabilization task of the magnetic levitation system. Complete procedure from derivation of a linearized model to controller design and tuning is described in detail. Finally the methodology proves useful for both stabilization in different operating points and output/load disturbance attenuation. Keywords—Algebraic approach, Magnetic levitation system, Robust control, Sensitivity functions, Unstable systems.