Applications of Lyapunov functions in the design of adaptive control for PLL systems

A model-reference adaptive control based on Lyapunov theorem is proposed for controlling several phase-locked loops (PLLs) from a single control voltage. The gain parameters of each linear oscillator (of the PLLs) in the system is identified and a control scheme is computed to minimize the phase error at the main control loop. A linear control law to reduce the control efforts to stabilize complex arrangement of nested or linked phase-locked loops is developed and applied to three different PLL systems operating at 1 MHz, 4 MHz, and 10 MHz whose v_in-ω characteristics are Lyapunov functions. Linear transformations were used to generate the linear control voltage that drives the discrete nonlinear points of the transfer characteristics. Summary of results for the three PLL examples is included