Designing Stable Control Loops The objective of this topic is to provide the designer with a practical review of loop compensation techniques applied to switching power supply feedback control。 A top-down system approach is taken starting with basic feedback control concepts and leading to step-by-step design procedures, initially applied to a simple buck regulator and then expanded to other topologies and control algorithms。 Sample designs are demonstrated with Math cad simulations to illustrate gain and phase margins and their impact on performance analysis。83563

 I。 INTRODUCTION

Insuring stability of a proposed power supply solution is often one of the more challenging aspects of the design process。 Nothing is more disconcerting than to have your lovingly crafted breadboard break into wild oscillations just as its being demonstrated to the boss or customer, but insuring against this unfortunate event takes some analysis which many designers view as formidable。 Paths taken by design engineers often emphasize either cut-and-try empirical testing in the laboratory or computer simulations looking for numerical solutions based on complex mathematical models。 While both of these approach a basic understanding of feedback theory will usually allow the definition of an acceptable compensation network with a minimum of computational effort。

II。 STABILITY DEFINED

Fig。 1。 Definition of stability

Fig。 1 gives a quick illustration of at least one definition of stability。 In its simplest terms, a system is stable if, when subjected to a perturbation from some source, its response to that perturbation eventually dies out。 Note that in any practical system, instability cannot result in a completely unbounded response as the system will either reach a saturation level – or fail。 Oscillation in a switching regulator can, at most, vary the duty cycle between zero and 100% and while that may not prevent failure, it wills ultimate limit the response of an unstable system。

Another way of visualizing stability is shown in Fig。 2。 While this graphically illustrates the concept of system stability, it also points out that we must make a further distinction between large-signal and small-signal stability。 While small-signal stability is an important and necessary criterion, a system could satisfy thisrt quirement and yet still become unstable with a large-signal perturbation。 It is important that designers remember that all the gain and phase calculations we might perform are only to insure small-signal stability。 These calculations are based upon – and only applicable to – linear systems, and a switching regulator is – by definition – a non-linear system。 We solve this conundrum by performing our analysis using small-signal perturbations around a large-signal operating point, a distinction which will be further clarified in our design procedure discussion。

Fig。 2。 Large-signal vs。 small-signal stability

III。 FEEDBACK CONTROL PRINCIPLES

Where an uncontrolled source of voltage (or current, or power) is applied to the input of our system with the expectation that the voltage (or current, or power) at the output will be very well controlled。 The basis of our control is some form of reference, and any deviation between the output and the reference becomes an error。 In a feedback-controlled system, negative feedback is used to reduce this error to an acceptable value –as close to zero as we want to spend the effort to achieve。 Typically, however, we also want to reduce the error quickly, but inherent with feedback control is the tradeoff between system response and system stability。 The more responsive the feedback network is, the greater becomes the risk of instability。 At this point we should also mention that there is another method of control – feedforward。With feed forward control, a control signal is developed directly in response to an input variation or perturbation。 Feed forward is less accurate than feedback since output sensing is not involved, however, there is no delay waiting for an output error signal to be developed, andfeedforward control cannot cause instability。 It should be clear that feed forward control will typically not be adequate as the only control method for a voltage regulator, but it is often used together with feedback to improve a regulator’s response to dynamic input variations。