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Computing

Faculty: Luca CorradiniPaolo Mattavelli

Introduction: Digital Controllers for Point-of-Load Regulators

Power converters for computing applications face unique challenges in terms of required dynamic performances. Digital loads such as microprocessors demand a tightly regulated supply voltage with extremely fast current slew rates. Analog-controlled power converters have usually offered the best dynamic capabilities for such computing applications. On the other hand, limited robustness and no field programmability is achieved by analog solutions.

Research of the Power Electronics Group in the field of Point-of-Load regulation has been focused on the development of digital controllers with analog-like performances, therefore providing the inherent versatilty of the digital implementation without compromising control requirements. Over the years, the research has led to pioneering works in the field of digitally controlled high-frequency power converters:

  • Digital multisampled controllers
  • Nonlinear Time-Optimal Control
  • Digital hysteretic control
  • Autotuning techniques for digital controllers self-calibration
       

Digital Multisampled Control for Point-of-Load Converters

Multisampled control aims at enhancing dynami c performances of digitally controlled power converters in applications where wide control bandwidth and tight output voltage regulation are crucial.

Conventional digital controllers for switched-mode power converters sample converter waveforms and update the control command once every switching period. In the process, small-signal delays of various nature arise which limit the achievable phase margin and control bandwidth. While A/D conversion and controller computational delays can be strongly optimized in a hardwired implementation of the controller, the PWM small-signal delay remains a major limiting factor for the control bandwidth.

The proposed digital multisampled control revises the conventional control architecture and operates the controller so as to acquire and process many samples per switching-period. In doing so, the PWM-related delay is roughly reduced by a factor equal to the oversampling ratio, allowing the digital architecture to achieve analog-like dynamic performances.

 

 

Our research on multisampled converters has developed along the following lines:

  • Use of ripple compensation techniques for practical implementation of wide-bandwidth multisampled controllers
  • Small-signal modeling of multisampled-converters
  • Large-signal nonlinear modeling of multisampled Pulse-Width Modulators

 


Architecture of a Digital Multisampled Controller with repetitive ripple compensation

0-15 A Step Load Response of a 4x Multisampled Digital Controller for VRM Applications with Adaptive Voltge Positioning

 

Robust Digital Time-Optimal Control

 


Block diagram of a Digital Time-Optimal Controller

The digital paradigm opens up the intriguing possibility of embedding nonlinear control actions into the system, capable of dramatically improving dynamic performances of the power converter. For Buck topologies, the fastest, or time-optimal response to an abrupt change in the load current is achieved through a properly timed on/off action of the main switch. Our research on time-optimal control has shown that the optimal control action can be carried out in a robust manner, i.e. in a way that is independent, to a first-order approximation, of the converter LC parameters.

The proposed controller architecture, sketched in the figure, consists of a conventional PID compensator for voltage regulation during steady-state, and a nonlinear time-optimal controller which takes over during load transients. The controller makes use of asynchronous A/D conversion in order to rapidly capture output voltage variations during a load transient. A simple digital finite state-machine coordinates the time-optimal switching action.

The technique, first formulated in the context of plain output voltage regulation, has been successively extended to embed Adaptive Voltage Positioning as required by modern microprocessors. Experimental tests have demonstrated the robustness of such parameters-independent time optimal controller against wide variations in the output filter capacitance.


Time-optimal response to a 0-8A step-up load transient


Time-optimal response to a 0-6.4A load step-up transient with Adaptive Voltage Positioning

Digital Hysteretic Control

Digital hysteretic control represents another nonlinear approach for boosting the dynamic performances of the digitally-controlled Point-of-Load regulator.

The control structure implements a high-bandwidth hysteretic differentiator as its main building block, and realizes a non-conventional structure of Proportional-Integral-Derivative (PID) compensation with performances comparable to analog hysteretic controls, thus breaking the bandwidth and dynamic limitations commonly encountered in typical digital control arrangements.

The employment of an asynchronous A/D converter based on the Threshold Inverter Quantization (TIQ) concept dramatically shrinks the average delay time which separates the sampling instant from the corrective control action. Moreover, the hysteretic nature of the derivative action results in an inherent nonlinear response to large signal load variations, which translates into fast control intervention and reduced settling times.

The hysteretic differentiator employs a ring-oscillator based modulator which ensures resolution up to 390ps without asking for a high-frequency clock. Both the 6-bit asynchronous A/D converter and the ring-oscillator based modulator are designed and manufactured in the same integrated circuit using a standard 0.35um CMOS process. Analytical modeling, computer simulations and experimental results on a synchronous buck converter confirm the validity of the approach and the dynamic performances achievable by the proposed control architecture.


Picture of the integrated asynchronous A/D converter
and ring oscillator-based DPWM


Block diagram of the proposed digital hysteretic controller


Closed-loop response to a 0-8A step load transient

Digital Autotuning Techniques


Block diagram of closed-loop model reference-based tuning

 

Autotuning, i.e. the capability of automatically calibrating the compensation parameters, is perhaps the most strikingly appealing advantage of digital control versus analog solutions. To put such potential advantage into practice, however, strongly optimized solutions must be formulated to limit the controller complexity without sacrificing tuning accuracy and robustness.

Our research has focused on two main classes of low-complexity autotuning solutions:

  • Autotuning techniques based on digital relay feedback
  • Model reference-based autotuning approaches

In the closed-loop model reference-based tuning system depicted in the figure, a perturbation frequency generated digitally is injected into the control loop and superimposed to the duty cycle command. The tuning is performed elaborating the signals right before and right after the injection point, and adjusting the PID parameters until predefined bandwidth and phase margin targets are obtained.The proposed approach allows for a robust and repeatable tuning, mainly because of the high resolution and dynamics available at the signal injection point. Moreover, the tuning is performed maintaining the closed-loop configuration, thus ensuring voltage regulation even during the PID adjustment, this being a fundamental constraint for most electronic equipments.


Example of system loop gain before and after the tuning process

 


Post-tuning closed-loop response to a 0-6A step load transient
with a digital Proportional-Derivative compensation

Publications

  • L. Corradini, P. Mattavelli, S. Saggini, “Elimination of Sampling-Induced Dead Bands in Multiple-Sampled Pulse-Width Modulators for DC-DC Converters,” IEEE Trans. Power Electron., vol. 24, no. 11, pp. 2661-2665, Nov. 2009
  • L. Corradini, A. Costabeber, P. Mattavelli, S. Saggini, “Parameter-Independent Time-Optimal Digital Control for Point-of-Load Converters,” IEEE Trans. Power Electron., vol. 24, no. 10, pp. 2235-2248, Oct. 2009
  • L. Corradini, E. Orietti, P. Mattavelli, S. Saggini, “Digital Hysteretic Voltage-Mode Control for DC-DC Converters based on Asynchronous Sampling,” IEEE Trans. Power Electron., vol. 24, no. 1, pp. 201-211, Jan. 2009
  • L. Corradini, W. Stefanutti, P. Mattavelli, “Analysis of Multisampled Current Control for Active Filters,” IEEE Trans. Ind. Appl., vol. 44, no. 6, pp. 1785-1794, Nov. – Dec. 2008
  • L. Corradini, P. Mattavelli, W. Stefanutti, S. Saggini, “Simplified Model Reference-based Autotuning for Digitally Controlled SMPS,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1956-1963, Jul. 2008
  • L. Corradini, P. Mattavelli, “Modeling of Multisampled Pulse Width Modulators for Digitally Controlled DC-DC Converters,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1839-1847, Jul. 2008
  • L. Corradini, P. Mattavelli, E. Tedeschi, D. Trevisan, “High-bandwidth Multisampled Digitally Controlled DC-DC Converters Using Ripple Compensation,” IEEE Trans. Ind. Electron., Special Section on FPGAs used in Industrial Control Systems, vol. 55, no. 4, pp. 1501-1508, Apr. 2008
  • W. Stefanutti, P. Mattavelli, S. Saggini, M. Ghioni, "Autotuning of Digitally Controlled Buck Converters based on Relay Feedback," IEEE Trans. Power Electron., Vol. 22, No. 1, pp. 199-207, Jan. 2007