Control basic building block( CB3) (Part II: rigid, invariant and chattering-free control of nonlinear and nonstationary systems)

A control system synthesis that provides rigid and invariant and at the same time chattering-free control in a general case of a nonlinear and nonstationary plant is presented. The synthesis makes use of a generalized multiple-input multiple-output (MIMO) control basic building block (CB³) which enables the system to track the reference vector with zero error in the presence of both external disturbances and plant uncertainties. The synthesis method is shown superior to the current adaptive control methods as well as the variable structure control (VSC) method, based on a generating control vector which controls the movement of the system states vector in the boundary layer about sliding hypersurfaces, in that once its multivalued control vector function, generated by the CB³, enters the rigid motion trajectory from the initial state by moving in a smooth (chattering-free) fashion along the sliding hypersurface in the state space, it then stays there assuming, in a continuous manner, any value necessary to maintain zero error. It is the multi-valued and nonswitching/continuous property of the control vector function for zero error that makes the proposed method distinguishable and superior to other types of control. The work also includes elaboration on practical aspects of the applications