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Posted on 30 May 2019

Fast Compensator Design and Optimization for Power Converters based on Graphical Visualization

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Shaping the control-to-output frequency response is a widely used technique for compensator design. The most important factors of the design process are phase margin (PM) and cross-over frequency (fc). Are all combinations of phase margin and cross-over frequency feasible? Can a high cross-over frequency and a phase margin of 45º always be achieved? Under uncertainties, is slow dominant-pole compensation the best solution?

By Antonio Lazaro and Andres Barrado, Carlos III University of Madrid; Hua Jin, Powersim Inc.

The proper selection of the phase margin and the cross-over frequency will enable the compensator synthesis and achieve good dynamical performance of the control loop. Bode plots are very useful. However, the complete loop performance analysis and PM–fc viability requires Nyquist plots and transient/steady state response plots. SmartCtrl, a CAD tool for analog and digital compensator design, shows that by means of interactive plots, all the information can be used effectively to carry out and optimize the compensator design.

Design Challenges

Each power converter presents a unique challenge in compensator design, depending on the topology type and the mode of operation (i.e. continuous conduction mode vs. discontinuous conduction mode). Designing the compensator of a Buck or Buck–derived converter (Forward, inverters, etc.), for example, is quite different and easier than designing the compensator for Boost or Flyback converter families.

Designers also face a series of design choices and tradeoffs. Which type of compensators is the most suitable: PI, PID, or something else? What is the right combination of the phase margin and cross-over frequency for the best stability and dynamic performance? Is one tenth of the switching frequency in voltage mode control the limit, and can it be pushed higher? Often, a PI or single pole compensator is placed below the resonance frequency. This is a slow, but stable solution. But does it always present a smooth transient-response?

PM-fc Constraints

Selecting the right phase margin and crossover frequency combination is a particularly critical design consideration. Synthetizing a PI compensator to have the fc value below the resonance frequency, for example, may result in the loop response crossing the 0 dB line several times and the actual fc below the one expected. Bode Plots are required to check this problem.

Most of the time, an analog compensator is made by means of an inverting amplifier. If fc is placed below the resonance frequency, the inverting amplifier compensator introduces an additional zero in the reference-to-output transfer function, causing a highly underdamped response. In this case, it is necessary to check time-domain transient response.

If the phase margin and cross-over frequency combination is selected in such a way that the phase of the control-to-output transfer function crosses below -180º for frequencies lower than fc, the control loop is only conditionally stable. This could cause a problem during start-up or at certain operating points of the converter. Again, Bode Plots visualization is an efficient way to anticipate this problem.

An additional constraint arises when a designer pushes for a high bandwidth. With a higher cross-over frequency, the output voltage ripple may not be attenuated sufficiently, and as a result, a higher ripple level could appear at the output voltage of the compensator. Since this voltage is expected to be close to a dc quantity, the ac component can cause fast scale instability or subharmonic oscillations when it is compared with carrier signal in the PWM modulator.

In this case visualization of time-domain waveform of the voltage at the compensator output helps greatly to avoid this problem.

Interface of SmartCtlr

Solution

To address the design challenges of the compensator design, a graphical tool called SmartCtrl is developed to visualize interactively and conveniently all key plots (Bode Plot and Nyquist plots) and waveforms (including transient response, steady state response, compensator output, etc.) in one environment. In particular, to address the phase margin and cross-over frequency constraints, a Solution Map is provided to show a valid design region within which a stable design can be achieved. Also, when a design parameter is changed, all the plots and waveforms are updated instantaneously with all the aforementioned constraints taken into account. Figure 1 shows the interface of SmartCtrl.

Sensitivity analysis of any parameter of the converter or the compensator can also be performed, including digital control effects such as digital delay and rounding effects. With the visualization of all vital information and the capability to carry out sensitivity analysis, designers can perform compensator design and optimization effectively and with confidence.

As the output, SmartCtrl provides the R-C values and coefficients of s-domain or z-domain transfer function blocks for analog and digital controllers. Finally, SmartCtrl is seamlessly integrated with the simulation software PSIM to validate the large signal performance, closing the complete design cycle.

 

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