The paper presents the problem of position control of DC motor with rated voltage 24 V loaded by flywheel. The fractional order PD controller implemented in National Instruments NI ELVIS II programmed in LabView is used for controlling. The simple method for determining stability regions in the controller parameters space is given. Knowledge of these regions permits tuning of the controller and ensures required the phase margin of the system.
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.