**2.3. Voltage control**

Control of switching power converters requires modulating the width of the pulse provided to the power devices' gate, based on feedback from the load voltage and the inductor's current. Fig. 5 illustrates the basic components of an analog control scheme; where the output voltage provides the desired feedback. This scheme is identified as the "voltagemode" control. The low-pass filter (R3, C3) of the error amplifier along with R1 provide feedback gain and reduce harmonics. The PWM hardware can be a typical controllable IC and the Schmitt-trigger is to produce sharp edges for the power device's gate. Needed high gate current usually requires current amplification as well.

The compensator can be implemented with Op-Amps to realize desired dynamic characteristics for voltage recovery and regulation. Traditional compensators like PID, leadlag, and Sliding Mode Control (SMC) are all applicable. Digital control, however, provides flexibility in implementing sophisticated control schemes and mixed mode operations to achieve power saving and to possibly automatic controller tuning. Digital schemes also reduce magnetic interference effects which would most probably exist in applications that require DC-DC power conversion. Digital Signal Processors (DSPs), microcontrollers, and Field Programmable Gate Arrays (FPGAs) together with the Analog-to-Digital Converter (ADC) are widely used to implement digital controllers. However, high-speed highresolution ADCs are expensive and they are not easy to consolidate into an integrated circuit.

Design of the compensator requires transient analysis and solving the differential equations that describe each waveform. Retaining the instantaneous detailed characteristic of the circuit requires analysis of each mode of the switching cycle. This level of detail is usually not necessary for the design of the compensator. Averaging over a number of switching cycles provides viable approximate models (Forsyth & Mollov, 1998) which simplify the compensator design significantly. In this technique, the state equations for the RC circuit are written for both modes of the converter (ON and OFF). A combined state equations model is then formed using the weighted average of the state matrices of the ON and OFF models according to the duty ratio (D). The produced model is a set of two linear time-variant state equations which ignore ripple components. The time-variant effect is due to the presence of the control variable "D(t)" (varying duty-ratio) in the state matrices rather than being part of the input control variables vector. Since solving time-variant equations is difficult, further simplifications are required. Linearization techniques are then employed for specific operating conditions, resulting in small-signal state-space models (Johansson, 2004). These models facilitate frequency and time domain design methodologies.

**Figure 5.** Voltage Control of Buck-Boost Converter

140 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

Current and voltage waveforms will be shown in Section 4 for illustration.

gate current usually requires current amplification as well.

**Figure 4.** DC-DC Buck-Boost Converter

**2.3. Voltage control** 

circuit.

D/(1-D). The orientation of the diode is such that the load current is blocked while the inductor is charging during Ton. During Toff the inductor releases its energy to the load through the diode loop resulting in an opposite voltage polarity compared to that of the buck or boost configurations. The size of the storage element (L) is critical to facilitating the boost mode. To insure CCM, the inductor must be of a certain minimum size (Rashid, 2004).

Control of switching power converters requires modulating the width of the pulse provided to the power devices' gate, based on feedback from the load voltage and the inductor's current. Fig. 5 illustrates the basic components of an analog control scheme; where the output voltage provides the desired feedback. This scheme is identified as the "voltagemode" control. The low-pass filter (R3, C3) of the error amplifier along with R1 provide feedback gain and reduce harmonics. The PWM hardware can be a typical controllable IC and the Schmitt-trigger is to produce sharp edges for the power device's gate. Needed high

The compensator can be implemented with Op-Amps to realize desired dynamic characteristics for voltage recovery and regulation. Traditional compensators like PID, leadlag, and Sliding Mode Control (SMC) are all applicable. Digital control, however, provides flexibility in implementing sophisticated control schemes and mixed mode operations to achieve power saving and to possibly automatic controller tuning. Digital schemes also reduce magnetic interference effects which would most probably exist in applications that require DC-DC power conversion. Digital Signal Processors (DSPs), microcontrollers, and Field Programmable Gate Arrays (FPGAs) together with the Analog-to-Digital Converter (ADC) are widely used to implement digital controllers. However, high-speed highresolution ADCs are expensive and they are not easy to consolidate into an integrated

Design of the compensator requires transient analysis and solving the differential equations that describe each waveform. Retaining the instantaneous detailed characteristic of the circuit requires analysis of each mode of the switching cycle. This level of detail is usually not necessary for the design of the compensator. Averaging over a number of switching cycles provides viable approximate models (Forsyth & Mollov, 1998) which simplify the compensator design significantly. In this technique, the state equations for the RC circuit are In addition to the above explained voltage-mode control scheme, current-mode control can also be achieved by sensing the current of the switching power device or the energy storage element and integrating it into the main voltage control loop (Johansson, 2004). In this scheme, the output of the voltage compensator acts are the reference voltage for the current feedback loop which controls the PWM and adjusts the gate pulse for the power device. This scheme usually improves the stability of the converter in high performance applications. Controlling the peak inductor current is one of the popular schemes employed. Current sensing can also be used to determine when to switch between CCM and DCM which facilitates implementing high efficiency schemes for operation.
