Aside 2. Design of the Analog PI Current Controller
2.3.2 Nonlinear Current Control: Hysteresis Control
The PI controller discussed above is not the only possible solution to provide the VSI of Fig. 2.1 with a closed loop current control. Other approaches are viable, among which the hysteresis current controller is the most successful. Even if we are not going to develop this topic in detail, we still would like to briefly describe the principles of this type of analog current controller, just not to give to the reader the wrong feeling that analog current control only amounts to PI regulators and PWM.
It is important to underline from the start that the hysteresis controller is a particular type of bang-bang nonlinear control and, as such, the dynamic response it is able to guarantee is extremely fast; actually it is the fastest possible for any VSI with given dc link voltage and output inductance. The basic reason for this is that the hysteresis controller does not require any modulator: the state of the converter switches is determined directly by comparing the instantaneous converter current with its reference. A typical hysteresis current controller is depicted in Fig. 2.12.
As can be seen, an analog comparator is fed by the instantaneous current error, and its output directly drives the converter switches. Thanks to the VSI topology and to the fact that the dc linkVDCvoltage will always be higher than the output voltage ESpeak value, the current derivative sign will be positive any time the high-side switch is closed and negative any time the low-side switch is closed. This guarantees that the controller organization of Fig. 2.12 will maintain the converter output current always close to its reference. Under the limit condition of zero hysteresis bandwidth, the current error can be forced to zero as well:
unfortunately this condition implies an infinite frequency for the switch commutations, which is, of course, not practical. In real-life implementations, the hysteresis bandwidth is kept sufficiently small to minimize the tracking error without implying too high switching frequencies. As a consequence, also the compensation of dead-time induced current distortion will be very good.
REFERENCES 31
LS RS
+
- 1
0
ES
+
-VDC
+VDC
IO IO
IOREF
FIGURE 2.12: Hysteresis current control hardware organization.
What is even more important, in the case of any transient, which may bring the instan- taneous current outside the hysteresis band, the controller will almost immediately close the right switch to bring the current back inside the band, thus minimizing the response delay and tracking error. Clearly, there is no linear controller that can be faster than this.
Nevertheless, the hysteresis current controller is not ubiquitously used in power electron- ics. That is because, despite its speed of response and high-quality reference tracking capabilities, this type of controller does have some drawbacks as well. The main is represented by a vari- able switching frequency. Indeed, any time the current reference is not constant the converter switching frequency will vary along the current reference period. The same holds in case the output voltageESis variable. The range of frequency variation can be very large, thus making the proper filtering of the high-frequency components of voltages and currents quite expensive.
Moreover, in the VSI applications like controlled rectifiers or active filters, the injection of a vari- able frequency noise into the utility grid is not recommended, because unpredictable resonances with other connected loads could be triggered. To solve this and other problems a considerable research activity has been developed in the last few years. Different control solutions, which try to keep the benefits of the hysteresis controller and, for example, get a fixed switching frequency out of it, have been proposed. We are not going to deal with this advanced topics. However, the interested reader can find much useful information in technical papers such as [12] or [13].
REFERENCES
[1] ISOSMARTTMHalf Bridge Driver Chipset, IXBD4410/4411 Data sheet and Appli- cation note,C 2004, IXYS website.
[2] N. Urasaki, T. Senjyu, K. Uezato and T. Funabashi, “An adaptive dead-time compensation strategy for voltage source inverter fed motor drives,”IEEE Trans. Power Electron, Vol.
20, No. 5, pp. 1150–1160, 2005.doi.org/10.1109/TPEL.2005.854046
[3] A. R. Munoz and T. A. Lipo, “On-line dead-time compensation technique for open-loop PWM-VSI drives,”IEEE Trans. Power Electron., Vol. 14, No. 4, pp. 683–689, 1999.
[4] N. Mohan, T. Undeland and W. Robbins,Power Electronics: Converters, Applications and Design. New York: Wiley, 2003.
[5] J. Kassakian, G. Verghese and M. Schlecht,Principles of Power Electronics. Reading, MA:
Addison-Wesley, 1991.
[6] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd edition.
Berlin: Springer, 2001.
[7] R. D. Middlebrook, “Predicting modulator phase lag in PWM converter feedback loop,”
Adv. Switched-Mode Power Convers., Vol 1, pp. 245–250, 1981.
[8] D. M. Van de Sype, K. De Gusseme, A. P. Van den Bossche and J. A. Melkebeek, “Small- signal Laplace-domain analysis of uniformly-sampled pulse-width modulators,”In 2004 Power Electronics Specialists Conference (PESC), 20–25 June, pp. 4292–4298.
[9] D. M. Van de Sype, K. DeGusseme, A. R. Van den Bossche and J. A. Melkebeek, “Small Signal Z-domain Analysis of Digitally Controlled Converters,”IEEE Trans. on Power Electron., Vol. 21, No. 1, pp. 470–478, 2006.
[10] G. C. Verghese, M. E. Elbuluk and J. G. Kassakian, “A general approach to sampled-data modeling for power electronic circuits,”IEEE Trans. Power Electron., Vol. 1, pp. 76–89, 1986.
[11] G. R. Walker, “Digitally-implemented naturally sampled PWM suitable for multi- level converter control,” IEEE Trans. Power Electron., Vol. 18, No. 6, pp. 1322–1329, 2003.doi.org/10.1109/TPEL.2003.818831
[12] Q. Yao and D. G. Holmes, “A simple, novel method for variable-hysteresis-band current control of a three phase inverter with constant switching frequency,” inConf. Rec. IEEE- IAS Annual Meeting, Toronto, ON, Canada, Oct. 1993, pp. 1122–1129.
[13] S. Buso, S. Fasolo, L. Malesani and P. Mattavelli, “A dead-beat adaptive hystere- sis current control,” IEEE Trans. Indust. Appl., Vol. 36, No. 4, pp. 1174–1180, 2000.doi.org/10.1109/28.855976
33
C H A P T E R 3
Digital Current Mode Control
In this chapter we begin the discussion of digital control techniques for switching power convert- ers. In the previous chapter, we have introduced the topology and operation of the half-bridge VSI and designed an analog PI current controller for this switching converter. Referring to that discussion, the first part of this chapter is dedicated to the derivation of a digital PI current controller resembling, as closely as possible, its analog counterpart. We will see how, by us- ing properdiscretizationtechniques, the continuous time design can be turned into a discrete time design, preserving, as much as possible, the closed loop properties of the former. It is important to underline from the beginning that the continuous time design followed by some discretization procedure is not the only design strategy we can adopt. Discrete time design is also possible, although its application is somewhat less common: as we will explain, its typical implementations rely on the use ofstate feedback and pole placement techniques. The second part of the chapter will describe in detail a remarkable example of discrete time design and, in doing so, it will also show how the synthesis of regulators that have no analog counter- part whatsoever can be implemented. This is the case of the predictive or dead-beat current controller.