In digitally controlled dc-dc converters with a single voltage feedback loop, the two quantizers, namely the analog-to-digital (A/D) converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of dc solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. Based on the generalized describing function method, the amplitude and offset-dependent gain model of a quantizer is applied to derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with A/D, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples

Modeling of Quantization Effects in Digitally Controlled DC–DC Converters

In digitally controlled DC-DC converters with a single voltage feedback loop, the two quantizers, namely the A/D converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of DC solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. A concept of amplitude and offset dependent gain is introduced to extend the describing function method and derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with A/D, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples.

Modeling of quantization effects in digitally controlled DC-DC converters

The conditions for limit-cycle oscillations in digitally controlled resonant converters are explored theoretically and are tested by simulation and experiment. The analytical analysis reveals that in a manner similar to digital pulsewidth modulation (PWM) control, limit cycles occur in such systems when the LSB of the control changes the output by a value that is larger than the analog-to-digital converter (ADC) resolution. However, in resonant converters, unlike the case of PWM, limit-cycle oscillations depend on the steady-state control input, since both the power stage gain and the resolution of the digitally generated drive frequency are not constant over the operating frequency range. Consequently, at high gains (close to resonance), the required frequency resolution may not be supported by the digital core. A time-domain behavioral simulation model, developed, and experimentally verified, allows the steady-state behavior of digitally controlled resonant converters to be analyzed, including the phenomenon of limit cycles as well as the closed-loop response. A cycle-by-cycle Powersim (PSIM) simulation model of a digitally controlled resonant converter, developed in this study, includes a digital core realization using C code block. This simulation model enables the exploration of the system in fine details. The proposed method of static analysis and dynamic modeling is experimentally verified on a series-resonant parallel-loaded converter operated in closed-current loop. The digital control algorithm was implemented on a TMS320F2808 DSP core. Very good agreement is found between the analytical derivations, simulations, and experimental results.

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Digital Control of Resonant Converters: Resolution Effects on Limit Cycles

An auto-tuning adaptive digital controller with maximum efficiency point tracking to optimize dc-dc converter switching frequency is presented in this paper. The adaptive-frequency-optimization (AFO) controller adjusts the dc-dc converter switching frequency while tracking the converter minimum input power (maximum efficiency) point under variable operation conditions of the power converter. The AFO digital controller continuously finds the optimum switching frequency that will result in minimum total power loss while converter parameters and conditions vary. Moreover, the presented controller addresses the issues that are associated with implementing variable switching frequency in digital controllers, including limit cycle oscillation and possible performance degradation, by using a dynamic algorithm to maintain converter system stability under variable switching frequency operation. In this paper, the proposed controller is discussed, analyzed, and its digital control algorithms and experimental results are presented.

Adaptive Digital Controller and Design Considerations for a Variable Switching Frequency Voltage Regulator

This paper presents numerical studies of analyses of the limit cycle of the reaction control system (RCS) and their validations through hardware-in-the-loop simulation (HILS). The numerical analyses under external disturbance and time-delays of the thruster are confirmed experimentally by HILS for an attitude control system with a single degree of freedom. The thrust of each jet thruster is determined from offline vacuum test results instead of actual thrust measurement. The comparison of HILS results with numerical analysis, shows that predicted properties of the limit cycle is closed to the test results, thus it can be applicable to real RCS. The HILS method allows us to test the RCS without an air-bearing system.

Hardware-in-the-Loop Simulation for the Reaction Control System Using PWM-Based Limit Cycle Analysis

The describing function method can be used to analyze control systems with separable nonlinearities. Here, the method is employed in conjunction with some of the robustness tools for linear systems to develop algorithms for predicting the existence of limit cycles in uncertain systems with multiple nonlinearities connected in series. Uncertainty is assumed to exist in terms of parameter variations in both the linear and the nonlinear elements. Examples are provided to illustrate the results which are, of course, subject to the usual errors and restrictions of the describing function method.

http://ieeexplore.ieee.org/iel5/7709/21120/00980387.pdf

N. Munro

Papers

Limit cycle analysis of uncertain control systems with multiple nonlinearities