Abstract. This paper presents the design of a robust PID controller for a four quadrant DC to AC switched mode inverter, using a buck- boost DC to DC converter.
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Robust PID Control of a Buck-Boost DC - AC Converter Ram6n Caceres, Rub& Rojas and Oscar Camacho Universidad de 10s Andes, Facultad de Ingenieria Escuela de Ingenieria EICctrica. AV. Tulio Febres Corder0 Merida 5 101 - Venezuela. e-mail: rcaceres0,ing.ula.ve Abstract This paper presents the design of a robust PID controller for a four quadrant DC to AC switched mode inverter, using a buckboost DC to DC converter. The designed controller is intended to decrease the total harmonic distortion (THD) in the output voltage against sudden load changes. The proposed robust controller is based in a classical two degree of freedom approach. The controller performance was tested by computer simulations.
1.
Looking forward to solve this problem using a simple classical approach, the performance of a robust control scheme based on a PID controller with two degrees of freedom is presented. This work is divided as follows: Section I1 presents the inverter scheme, in Section 111 the robust PID design, Section IV some simulation results. Finally the conclusions are presented.
Introduction
2.
The buck-boost inverter is a highly nonlinear scheme intended to be used in UPS design, whenever an AC voltage larger than DC link voltage is needed, with no need of a second power conversion stage. This inverter is a four quadrant DC to AC switched mode inverter, using buckboost DC to DC converter [l]. The main attribute of this inverter topology is the fact that it naturally generates an AC output voltage lower or larger than the DC input voltage, depending on the instantaneous duty - cycle. This property is not found in the classical voltage source inverter which produce an AC output instantaneous voltage always lower than the input DC voltage.
Inverter Scheme
The inverter scheme is configured on the current bidirectional buck-boost converter. The circuit implementation of the buck-boost DC to AC converter is shown in Fig. 1. The buck-boost inverter achieves DC - AC conversion as follow : This buck-boost inverter is composed by two bidirectional buck-boost converters. These converters produce a DC-biased sine wave output, so that each converter produces a unipolar voltage. The modulation of each converter is 180 degrees out of phase with respect to the other, which maximizes the voltage across the load. The load is connected differentially across the converters. Thus, a DC bias appears at each end of the load with respect to ground, then differential DC voltage across the load is zero. The generating bipolar voltage is solved by a push-pull arrangement. Hence, the converter current will be bidirectional, and should be taken into account in the implementation.
Because of its nonlinear behavior and the presence of sudden load changes when the inverter is in operation, particular attention must be pay in its control. When classical PID control is used the output voltage shows a THD less than 5 % against small load changes but when the load is suddenly decreased above 30% of the nominal load the system becomes unstable [ 2 ] .
I
Vin
t L
v2
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R
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Figure 1. The DC - AC Buck-Boost Converter
0-7803-6407-4/0~5/$10.00 @2000 IEEE
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Mathematical Model
2.1
Using the average concepts, the following voltage relationship for the continuous conduction mode: is obtained
The process begins by substituting the DC model and then solving for the DC operating point. These DC quantities are then used as an input to the fundamental frequency model which is next substituted for the PWM switch.
v, -- D v,,, 1- D
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~~
.
I?
c
where D is the duty cycle. The voltage gain, for the buck-boost inverter, can be derived as follows: Assume that the two converters are 180 degrees out of phase. Then, the output voltage can be obtained as:
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2
(3)
The nonlinear characteristic gain of the buck-boost inverter is shown in Fig. 2. Notes that the feature of zero output voltage is obtained for D = 0.5. Therefore, if the duty cycle varies around this point, then an AC output voltage across the output terminal is obtained.
A
Di3
Figure 3. (a) The PWM Switch, (b) DC Model and (c) Fundamental Frequency Model of the PWM Switch.
R
Figure 4. Shows the Equivalent Circuit for the Buck-Boost Inverter, with the Three-Terminal PWM Switch.
Figure 2. DC Gain Characteristic.
The DC and Small-Signal performance of a buck-boost DC to AC converter is determined substituting the PWM switches by their respective linear circuit models [3], [4]. These circuit models are shown in Fig. 3 for DC and the fundamental frequency. After determining the DC operating point, the output voltagekontrol transfer hnction is obtained.
By substituting the DC model of the PWM switch into the buck-boost inverter of Fig. 4, results in the circuit shown in Fig. 5. In this circuit all the reactive elements have been shorted or opened as required at zero frequency.
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Va
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+
Vb
Zu( S ) =
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