The huge influence of the sampling rate on the performance of the digital PID control of a voltage source inverter (VSI) is revealed. It is shown that an appropriately chosen continuous-time model of a digital controller with the PWM power converter behaves like the actual discrete-time system, which allows for a simple controller analysis and design. The variable structure nature of the inverter with both the RC rectifier and an abruptly changing resistive load with two modes of operation within the sampling period is directly taken into account. Two simulation models, a discrete-time PWM and a continuous-time, of an inverter are presented, which are used to tune the PID controller and to evaluate the control performance. The behavior of the system in both modes is explained on the basis of the root loci and frequency characteristics. The results obtained for three sampling rates: 12.8, 25.6, and 51.2 kHz, are presented and compared with an actual VSI experiment. A comparison with other results obtained for this VSI shows that properly tuned PID control outperforms the more sophisticated solutions based on the coefficient diagram method (CDM) and the passivity based control (PBC).

The article considers the step and impulse response of second-order linear systems with a positive zero. A particular parameterization of the system equations is proposed which enables good assessment of the influence of its parameters on transients. Expressions missing in the literature are derived for step response parameters such as the values of undershoot, overshoot, time of inverse response, rise time and settling time, as well as of impulse response. Based on them, a precise time-domain approach to design feedforward, feedback and mixed feedback– feedforward control structures for nonminimum phase objects is presented that considers both setpoint tracking and disturbance rejection.

The concept of hybrid control has been introduced, in which the analog implementation of the control algorithm is combined with a digital algorithm for determining the PWM duty cycle. Single-loop PD and PID control systems are compared to a double-loop architecture with additional capacitor current sensing for both digital and hybrid controller realizations. The performance is measured as the THD value under resistor-capacitor rectifier load. It has been shown that a properly constructed continuous-time model of a digital controller with a PWM power converter behaves like the actual discrete-time system, which allows for a simple controller analysis and design. The role of a PWM type for capacitor current feedback is emphasized. The simulation models of a real inverter are presented, which are used to tune the controllers and to evaluate the control performance for both rectifier and abruptly changing resistive load. The obtained solutions achieve the THD values comparable to the VSI without load. The results are contrasted with the control methods based on resonant filters.