A pulse-width-modulated (PWM) output followed by a first-order resistor–capacitor (RC) filter provides a low-cost approach to digital-to-analog conversion. This paper develops a resolution expansion of a reference expression for the continuous rising-transition settling count in the parameter δ = 2^−N, retaining the tolerance ε exactly. Here N denotes the resolution, and ε is expressed as a fraction of one least significant bit. The coefficients contain half-integer powers of ε and therefore have a Puiseux-type form. The first-order expression removes the exponential quotient of the reference expression and makes the dependence on N and ε explicit. Two higher-order truncations are also derived. For 1/8 ≤ ε < 1/2, the first and second truncations are proved never to underestimate the reference count. Both coincide with it at ε = 1/8. Over 1122 combinations with N = 4–20 and ε = 0.125–0.45, the maximum errors relative to the reference count are 0.21, 0.050, and 0.0025 PWM periods, with rounded-count agreement of 89.66%, 99.82%, and 100%, respectively. At every tested combination, the reference expression and the exact first-order model give the same rounded rising-transition count, and adding one period to each rounded truncated count covers the exact worst-case count over both transition directions. Both results are numerical and are established only for the tested grid.

This paper shows the possibility of implementing model predictive control algorithm as rate autopilot for guided aerial bomb. Mathematical model that is used for transfer function estimation and simulation of the bomb flight is presented. Transfer functions are estimated at different time instants during the flight. Model predictive controller and PID controller were designed for rate autopilots and simulation results are compared.

This paper presents the implementation and experimental validation of a current regulation method for a brushless DC motor driven by a trapezoidal, six-step commutation scheme. The proposed approach uses a series-form PI controller designed from a first-order electrical model of the motor winding. The method is implemented on a custom motor driver using Hall sensor commutation, unipolar PWM switching, synchronized ADC current sampling, and digital current filtering. Experimental step responses for several calculated gains show stable current regulation with negligible steady-state error. The presented approach provides a simple and practically applicable tuning procedure for BLDC current loops using trapezoidal commutation.