Stability analysis of pulse-width-modulated feedback systems

A theory is developed to predict the stability characteristics of static converters as a function of the controlled-firing angle for closed-loop systems using an integrating controller. The controlled quantity can be either the output voltage or current. Revealed in the analysis was how the degree of stability is dependent on the operating point, the waveform and pulse number of the supply, the commutating reactance, and the method of modulating the firing angle. The factors that determine stability are related to the step change in the output voltage waveform at the instant of switching. In practical application of the theory, the closed-loop performance can be improved by suitably shaping the modulating function or `firing wave'. It is found that the optimum shape of the firing wave is not the same shape that produces a linear open-loop voltage gain.

The closed-loop stability of power converters with an integrating controller

Stability analysis is of great significance in those feedback control systems in which the power amplifier is operated as a pulse-modulator device, since under these circumstances the whole control system is highly non-linear. Stability in PWM feedback control systems with a proportional type regulator has been amply described in the literature. Only recently, however, have such studies been extended to include systems with a proportional-plus-integral regulator. In this paper the problem is considered for the case involving a PWM control system, where the regulator is a proportional-plus-integral-plus-derivative, the PWM modulator is of a very general type and the controlled process is of arbitrary order. The stability of the system is analysed by means of a discrete version of the second Lyapunov method ; this method in turn leads to an investigation of the positivity region of a quadratic form defined in the parameter space of the regulator. To improve the stability region obtained, a procedur...

Stability analysis of PWM feedback control systems with PID regulators

Distributed control of multi-agent systems with pulse-width-modulated controllers

This chapter introduces electrochemical corrosion kinetics of metallic systems. It starts by presenting basic interfacial electrochemical polarization aspects and the corrosion relevance. It then explains mixed potential theory, reversible electrode potential, exchange current density, corrosion potential, corrosion current, and Tafel slopes. A full discussion on ohmic and electrochemical polarization, special cases of the Butler-Volmer equation with high and low field approximation and concentration polarization are included to show the relationship to polarization behavior and mass transfer. By the end of the chapter, solved and exercise problems illustrate reaction kinetics analyses at the metal-solution interface, corrosion process mechanisms, corrosion rate control, and corrosion protection strategies.

Electrochemical Kinetics of Corrosion

A unified approach to stability analysis of feedback control systems with pulse-width modulators is discussed. The proposed procedure is developed on the basis of the discrete analog of Lyapunov's method, with no limiting hypothesis on the structure of the controlled plant and of the modulation law. The analysis is exemplified particularly for lead-type PWM control systems. Significant plant classes are investigated, and the critical values of parameters in a closed form are determined which assure asymptotic stability of the steady-state solution, whatever the reference input may be.

A generalised approach to the stability analysis of PWM feedback control systems

Pulse Ratio Modulation: An Interesting Technique to Implement DC/DC Conversion

DC/DC converters may be considered as pulse modulators; the modulation laws usually implemented are those related to pulse frequency (PFM) and pulse width modulation (PWM) techniques. The pulse ratio modulation (PRM) technique, providing several advantages over conventional pulse modulation methods, has been developed for applications in a space vehicle attitude control system. Capable of operation with a high degree of precision and overcoming certain bandwidth problems associated with other modulation techniques, the modulator appears to hold excellent possibilities for applications in a broad range of control systems, such as DC and AC drives. In order to investigate the dynamical properties presented by a feedback control system employing this modulation technique, in the paper a mathematical model is presented, characterizing the PRM in terms of input output relationships. By using the state variables approach, the system is described through a vector recurrence equation and linear bounds on the state characterizing the adopted modulation law. On the basis of this model both the steady state behaviour and the transient response are evaluated. As far as stability properties are concerned, the linearized model is developed in order to determine the local behaviour in correspondence with the steady state solutions, and a comparison is made with an equivalent PWM control system. Moreover a procedure, based on the use of projection operators in vector spaces, is presented to analyse the asymptotic stability in the large.

A. Eisinberg

Papers

A generalised approach to the stability analysis of PWM feedback control systems

Pulse Ratio Modulation: An Interesting Technique to Implement DC/DC Conversion

Pulse ratio modulation : an interesting technique to implement dc/dc conversion

On the stability of thyristor phase-controlled converters

On the analysis of chopper drives with pulse width modulators