Chapter 1
INTRODUCTION
1.1 Background of the study
DC toDC Buck – – Boost converters are electronics circuits which convert a voltage from one level to a higher or lower one. Buck Boost converters are more and more used in some electronic devices such as DC-Drive systems, electric traction, electric vehicles, machine tools, distributed power supply systems and embedded systems to extend battery life by minimizing power consumption (Rashid, 2001). There are three topologies for designing a DC – DC converter. converter. The three topologies are buck, boost, and buck boost. These topologies are nonisolated, i.e the input and the output voltages share a common ground (Everett, 1999). Their application for power range from watts (mobile phones), kilowatts (DC motors), to megawatts (traction vehicles) (Ortuzar et al). The DC to DC converters are designed to work in open-loop mode. However, these kinds of converters are nonlinear. This nonlinearity is due to the switch and the converter component characteristics. For some applications, the DC-DC converters must provide a regulated output voltage with low ripple rate. In addition, the converter must be robust against load or input voltage variations and converter parametric p arametric uncertainties. Thus the output voltage must be performed in a closed loop control mode (Ben Saad et al., 2010). This takes us to the design of a controller. There are several control design used to control DC-DC Buck Boost converters. In the past years the DC – DC DC converters were controlled using analog integrated circuit technology and linear system design techniques. Conventional control techniques used
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for DC-Dc converters are PID controllers which tend to provide linear characteristics and therefore nonlinear controllers are often developed. It is always desirable for converters with constant output voltage that the output voltage remains unchanged in both steady and transient operations whenever the supply voltage voltag e and/or load current is disturbed. This condition is known as zero-voltage regulation; the choice of the control method plays a very critical role in the performance of converters. The most commonly used method in converters is the direct duty ratio control, but it is complex to practically execute. Another method is current control mode control, co ntrol, but these cannot eliminate the load current disturbances (Govindaraj et al., 2010 , Boumediene et al., 2011) the other mostly used are proportional integral and hysteretic control (Ben Saad et at., 2010).However, for some cases this control approach is not so efficient (Adams et al, 1992) and therefore, there is a greater interest in developing more advanced and nonconventional nonlinear robust control structures to improve the performance of buck boost DC to DC converters (Boumedieneet al., 2011). The fuzzy logic PI has been proposed to improve the robustness and dynamic response of buck boost converter. It provides an effective means of capturing the approximate, inexact nature of the real world (Govindaraj, 2011)
1.2 PROBLEM STATEMENT
Usually, the control problem consists in defining the desired nominal operating condition, and then regulating the circuit so that it stays close to the nominal, when the plant is subject to disturbances and modeling errors that cause its operation to deviate from the nominal. Unfortunately, PID control does not always fulfill these control specifications especially when disturbances rejection and transient response time requirement are concerned, due to the highly non-linear characteristics of DC – DC converters. As a result, microcontroller-based or DSP based approaches have been
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developed to implement advanced/improved control algorithms such as nonlinear PID (M.Lazer, et al, 2009) The other major problem challenging the design of buck boost controllers are
Right-Half plane zero
Chattering phenomenon
The converters nonlinearity.
A classical buck boost DC to DC converters suffers from the well-known problem of right-half-plane zero in its control to output transfer function under continuous conduction mode. The converter must first store the energy in the inductor during the rest of the cycle. If the duty cycle quickly changes in response to a perturbation, then the inductor naturally limits the current slew rate and the output voltage drops (power electronics. Com, accessed on (/22/2011). This forces the designers to limit the overall closed loop bandwidth to be much less than the cornerfrequency due to the worst case righthalf plane zero location, and as a result the system has a sluggish small signal response and poor large signal response (Jawhar et al., 2007, Mitchel, 2001). There are two possible routes to achieve fast dynamic response; first is to develop a more accurate non-linear model of the converter based on which the controller is designed, and the second one is to develop Artificial intelligence way of using human experience in decision making, i.e fuzzy logic (Jawhar et al., 2007) Another problem facing the controller of DC to DC converter is in frequency domain method for design of controllers where the small signal model of the converter has restricted validity and changes due to changes in operating point. Also the model is not sufficient to represent systems with strong nonlinearity. The causes of n onlinearity in power converters include a variable structure within a single switching period, saturating inductances, voltage clamping, etc. so whenever there is any changes in system, any parameter variations or even load disturbances PID controllers tend to be less. It is therefore always desirable that the converters output voltage remains unchanged in both
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steady and transient operations whenever the supply voltage or load current is disturbed. This condition is known as Zero-voltage regulation, which can be controlled by using direct duty ratio control, however this method is too complex to execute practically and so the designers have developed fuzzy logic controllers (Govindaraj et al., 2011). Chattering phenomenon is also a challenge in the design of controllers. For example, in the design of SMC law, it is assumed that the control can be switched from one value to another infinitely fast. However this is impossible to achieve in practical systems because finite time delays are present for control computation, and limitations exist in physical actuators. This non ideal switching results in a major problem called chattering phenomenon, which may excite high-frequencyunmodeled dynamics which can result in unforeseen instability, and also cause damage to actuators or plant (Jiunshian et al, 2007). However this problem can be solved by using Fuzzy sliding mode control (FSMC) (Sahbani et al, 2008).
1.3 AIM
The aim of this project is to develop and implement a buck-boost DC to DC converter and a duty cycle control of the switching signal given the converter using PI controller. 1.4 OBJECTIVES
The objectives of this project are;
Develop and implement a Buck-Boost DC to DC converter giving a regulated and stable output voltage.
Design and build a PI controller for the buck – boost DC to DC converter
Carry-out the simulation so as to analyze and investigate the response performance of the controller.
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CHAPTER 2
2.0 Introduction
In this chapter we are going to review other existing designed projects, that apply Fuzzy logic PI controller and PWM to control the Buck Boost converter, and get the related conceptual ideas and specifications that will help improve the control of buck boost to give a better and more stable performance. 2.1 Literature Review
DC to DC Converters are widely used in most of the applications. Several control strategies have been proposed in the past few years. A general purpose fuzzy controller is presented in (Mattavelli et al., 1997) to obtain a high performance voltage control in a buck boost converter. A robust controller based on a u-synthesis approach is presented in (Buso, 1999) using a linear model of Buck boost converter. A non-linear predictive control is used in (Lazar et al., 2008) that can be used for different topologies without changes in the controller structure. Nonlinear approaches based on SMC have been proposed (Garcia et al., 2009). Lazar et al.,developed a non-linear predictive controller for regulating DC-DC power converters. The proposed control strategy was implemented and tested using two models: an averaged non-linear model for control purposes and a switched Buck-Boost circuit model as the controlled plant. A comparison with classical PID control in terms of start-up behavior and robustness to disturbances was given in order to outline the performance of the predictive controller. From his results obtained he concluded that nonlinear predictive control algorithm ensures a much better performance than the one
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achieved with the tuned PI controller and that it guarantees a stable operation under ill conditions.
Fudil et al., focused on the problem of controlling buck boost converter by backstepping control approach. He designed both adaptive and non-adaptive which yielded interesting tracking and robustness performances. In his study he pointed out backstepping nonlinearcontrollers perform as well as passivity-based controllers, but later concluded that adaptive backstepping controllers are more interesting as they prove to be less sensitive to design parameters (Fudil et al.,).
Hebertt, proposed linearization techniques for the design of nonlinear proportional-integral (PI) controllers stabilizing, to a constant value, the average output voltage of pulse width modulation (PWM) switch – regulated DC to DC converter. He employed Ziegler Nichols method for the PI controller specification (Hebertt, 1991 ). (Skogestad and Wolf, 1992) made significant contributions to control analysis and to the study of the dynamic adaptability of systems, introducing and analyzing control magnitudes for the interaction of the variables and the rejection of disturbances in DC to DC converter.
Rasila et al, designed a fuzzy logic controller and compared the results obtained with results from conventional control algorithms. In his discussion he cited that FLC yields results superior to those of conventional control algorithms (Rasila et al., 2011). Yusuf et al, examined fuzzy logic based control of start-up current of a buck boost converter through computer simulations. For him to point out the advantages of fuzzy logic control, he compared the results with classical PI control under same circumstances. According to simulation he concluded that fuzzy logic control has stronger responses than PI control and uses lower current at starting moment (Yusuf et al., 2009).
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Mahdavi, Emadi and Toliyat designed sliding mode controllers for buck, boost, buck-boost and Cuk converters based on the state-space-averaging method. The controllers were simulated and satisfactory simulation results were obtained (Abdellah et al., 2011). Cortes and Alvarez investigated several sliding surface designs for boost converters. They proposed sliding surfaces that do not depend on the load to eliminate the necessity for current measurement. Vidal-Idiarte, Martinez-Salamero, et al. presented a two-loop control for a boost converter. An inner loop controlled the inductor current usingsliding mode control. The outer loop used a fuzzy controller to implement the voltage loop. The controller implementation used analog components for the inner loop and an 8-bit microcontroller for the outer loop (Sahbani., 2008).Orosco and Vazquez analyzed discrete sliding mode control for DC-DC converters. The analysis included the reaching condition, proof of the existence condition of the sliding mode and stability conditions. Simulation results were presented.Most research on sliding mode controllers for DC-DC converters has been limited to continuous time, and only simulation results have been presented. Furthermore, several disadvantages exist for sliding mode control. Because infinitely fast switching of thecontrol action is impossible in practice, chattering always occurs in steady state. A constant switching frequency can‟t be guaranteed. This issue has prevented sliding mode control from being extensively applied to DC-DC converters.
Gloria et al., in her theoretical study about traditionally design of controlled DC to DC converter she cited two steps. In the first step the structure of the system is defined and the components (capacitor, inductor, etc) are computed to obtain, in steady state, a desired set of specifications such as ripple, nominal voltage etc. in the second step a dynamical model of the converter is computed and a controller is tuned to achieve a set of transient specifications, such as rise time and over shoot. Sometimes the obtained closed-loop performance is not satisfactory as the adequate functioning of the DC-DC converter in closed loop, does not depend exclusively on the kind of controller
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and its parameters, since the control of a process is conditioned by its own design (Gloria et al., 2009).
Among the various techniques of artificial intelligence, the most popular and widely used technique in control systems is fuzzy control. Fuzzy controllers are designed based on the general knowledge of the converters. The controller is then tuned using a trial and error method to obtain satisfactory response. Since a fuzzy controller is a nonlinear controller, it can adapt to a varying operating point (Feshki, 2011 and Liping, 2007). Many researchers have investigated fuzzy controllers for DC-DC converters.
Farahani studied the development of fuzzy and PI, Simulation results were compared with the results of a PI controller under varying operating points. The performance of the fuzzy controller was superior to the performance of the PI controller in that the comparisons show that the fuzzy controller has faster dynamic when compared with the PI digital classic one.
Govindaraj et al and Ben Saad et al investigated a general-purpose fuzzy controller for DC-DC converters. The fuzzy controller improved performance in terms of overshoot limitations and sensitivity to parameter variations compared to standard controllers. Simulation results for buck-boost and Sepic converters were presented. The small signal model for the converters and linear design techniques were used in the initial stages of fuzzy controller design. Simulation and experimental results were presented and compared with results of a digital PI controller. Yusuf, Farahaniconcluded from the comparison of start-up responses and load regulation tests that the currentmode controlled buck converter had a faster transient response and better load regulation, while the fuzzy controller for both boost and buck-boost converters had less steady-state error and better transient response.
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Abdelaziz et al, proposed a Fuzzy Sliding Mode Control (FSMC) as a control strategy for Buck-Boost DC-DC converter. The proposed fuzzy controller specified changes in the control signal based on the knowledge of the surface and the surface change to satisfy the sliding mode stability and attraction conditions. Similarly, Boumediène et alfocused on the use of the fuzzysliding mode strategy as a control strategy for buck-boost DC-DC converter power supplies in electric vehicles. The satisfactory simulation results showed the efficiency of the proposed control law, which reduced the chattering phenomenon. Moreover, the obtained results prove the robustness of the proposed control law against variations in load resistance and input voltage in the studied converter.
Jawhar et al, proposed Neuro Fuzzy controller to improve the performance of the buck &boost converters. The duty cycle of the buck & boost converters are controlled by Neuro Fuzzy controller.
2.2 Theoretical Background
DC to DC Converters are used to convert the unregulated DC input toa controlled DC output at a desired voltage level. Switch-mode DC to DC converters includes buck converters, boost converters, buck-boost converters, Cuk converters and full-bridge converters, etc. Among these converters, the buck converter and the boost converter are the basic topologies. Both the buck-boost and Cuk converters are combinations of the two basic topologies. The full-bridge converter is derived from the bu ck converter.
There are usually two modes of operation for DC to DC converters: continuous and discontinuous. The current flowing through the inductor never falls to zero in the continuous mode. In the discontinuous mode, the inductor current falls to zero during the time the switch is turned off.
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2.2.1
Basic operation of buck-boost converter
The BBC is basically a DC to DC converter normally used as a power supply with
) that can be higher or lower than the supply voltage
adjustable output voltage (
). From the control point of view (Fuzzy logic PI and PWM), the objective of this
(
system is to provide an output that can follow a desired voltage reference and reject the disturbances caused by variations or rather take the error back to the input. To perform this task, an adequate control strategy actuating on the switch Q1 must be defined.
Figure 2.0Ideal Buck Boost converter
The BBC can operate in two different modes. If the current in the inductor L is not zero, then the BBC operates in continuous conduction mode. Otherwise, a discontinuous operation mode is considered (Garcia, et al, 2009). Continuous inductor current mode is characterized by current flowing continuously in the inductor during the entire switching cycle in steady-state operation. Discontinuous inductor current mode is characterized by the inductor current being zero for a portion of the switching cycle. It starts at zero, reaches a peak value, and returns to zero during each switching cycle.
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2.2.2
Buck converter
The Buck converter shown in Figure 2.1 converts the unregulated source voltage Vin
. The NPN transistor shown in Figure 2.1 works as a switch. The ratio of the ON time ( when the switch is closed to the entire switching period (T) is defined as the duty cycle The corresponding PWM signal is as into a lower output voltage
shown in Figure 2.2
Figure 2.1 buck converter Switching period (T)
ton
Figure 2.2 PWM signal to control switches in the DC-DC converter The equivalent circuit in Figure 2.3 is valid when the switch is closed. The diode is reverse biased, and the input voltage supplies energy to the inductor, capacitor and the load.
Figure 2.3 Equivalent circuit of the Buck converter when the switch is closed
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Figure 2.4 Equivalent circuit of the buck converter when the switch is open
When the switch is open as shown in Figure 2.4, the diode conducts, the capacitor supplies energy to the load, and the inductor current flows through the capacitor and the diode(rogers, 2002) the voltage output voltage over input voltage is D, which is given by
, (Guo, 2006) 2.2.3
Boost converter 2
D1
L1
C1
Q1
Vin
load
Vout
Figure 2.5 Boost Converter 7
L2 Q2 C2
Vin
load
Vout
Figure 2.6 Equivalent Circuit of the Boost converter when the transistor is closed L3
Vin
C3
load
Vout
Figure 2.7 Equivalent Circuit of the Boost converter when the transistor is on
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The boost converter shown in Figure 2.5, converts an unregulated source voltage Vin into a higher regulated load voltage Vout. When the switch is closed as shown in Figure 2.6, the diode is reverse biased and the input voltage supplies energy to the inductor while the capacitor discharges into the load. When the switch is opened as shown in Figure 2.7, the diode conducts and both energy from the input voltage and energy stored in the inductor are supplied to the capacitor and the load; thus the output voltage is higher than the input voltage (Rogers, 2002). During steady state operation, the ratio between the output and input voltage is
, which is given in Figure 2.2. The output
voltage is controlled by varying the duty cycle
2.3 Control of the system
In DC-DC converters the state of power switches are generally determined by Pulse Width Modulation (PWM) method. Also in this study PWM method has been used. In switching with PWM of constant switching frequency, switch control signal which determines whether the switch is turn on or off, is obtained by comparison between the control voltage at signal level (
) and the repetitive waveform () shown in Figure
2.8 Vst=Repetitive waveform
Vk
t
0
Vk > Vst Switch control signal
on
on
off
ton
Figure 2.8 Pulse width modulation waveform
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toff
off
Vk < Vst
) with a constant peak value and which is
The frequency of the repetitive waveform (
shown to be saw tooth, establishes switching frequency In case of controlling with PWM, this frequency value can be fixed and set to a value between a few kilohertz or a few hundreds of kilohertz. When amplified error signal, which varies very slowly with time relative to the switching frequency, is greater than the saw tooth waveform, the switch control signal becomes high, causing the switch to turn on. Otherwise, the switch is off (Mohan et al., 1989). As this prin ciple considered, converter‟s switching is being modeled within the frame of the reason shown below.
{
Control of the motor is performed by setting the DC input voltage of the motor. The input voltage of the motor is on the other hand, the output voltage of converter. The output voltage of converter is performed by setting of the control voltage, ( this paper, in order to set the (
) value. In
) value, PI and fuzzy logic control have been used and
the results of both of the control systems have been compared.
2.3.1
Voltage mode control
In voltage mode control, the converter‟s output voltage is compared with a reference to generate the voltage error signal. The duty cycle of PWM is adjusted based on the error signal to make the input voltage follow the reference value. Frequency response methods are usually used in the design of voltage mode controllers for DC to DC converters. The frequency of the PWM signal is the same as the frequency of the saw tooth waveform.
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The error amplifier reacts in a fast manner to changes in the converter output voltage. As a result, voltage control scheme provides good load regulation against variations in the load. However regulation against variations in the input voltage is delayed because changes in the input voltage must first manifest themselves in the converter output before it can be corrected. Figure 2.9, shows the block diagram for voltage control mode.
Figure 2.9Voltage mode control block diagram
Figure 2.10Signal pulse generated
The pulse width modulation circuit converts the output from the error amplifier and
. It‟s then compared with saw tooth waveform with amplitude
produce
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and the output from comparator is used at drive circuitry. It is shown in Figure 2.10 where the PWM is produced by comparing with (stefanutti, 2005). 2.3.2
Current control mode
An addition inner control mode loop feedback an inductor current signal and this signal are converted into its voltage analogue is compared to the control voltage. This modification of replacing the saw tooth waveform of the voltage mode control scheme by a converter current signal changes the dynamic behavior. The result of current mode control is a faster response and mainly applied to boost and buck-boost converters which suffer from an undesirable non-minimum phase response. With the inductor current taken into account, current mode control performs better, however the application of current mode control to the buck converter does not gain much benefit over voltage mode control. This is because the inductor current information can be readily derived from the output in the case of the buck converter. In addition, with the absence of the low frequency inductor current dynamics, the inheritances of non-minimum phase problem associated with the boost and buck-boost converters is automatically eliminated. High frequency instability in the form of sub harmonics and chaos is possible in current mode control. Figure 2.11 shows the block diagram of current mode control (pressman, 2009).
Current Compensator
Voltage Compensator
PWM Comparator saw tooth
DC reference
Verror
PWM Control
Signal from output Voltage feedback
inductor current
Rs
Compensation Network
Figure 2.11 Current mode control block diagram
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The voltage across the current sense resistor which represents the actual inductor current is fed into the current compensator and compared to the desired current program level. The difference or current error is then amplified and filtered. After that it is compared with saw tooth ramp at PWM comparator input to generate the required duty ratio. This control scheme also provides excellent noise immunity to the spike sensed in the inductor current. When the clock pulse turns the power switch ON, the oscillator ramp
immediately dives to its lowest level which means volts away from the
corresponding current error level at the input of the PWM comparator (Dixon L, 1990). 2.3.3
System Control by PI
Block diagram of system controlled by PI is shown in Figure 2.12. In order to reach the
are calculated. These variables are the inputs of PI control. Error and error change are calculated as shown below desired value error e(t), and error change
Figure 2.12 Buck Boost Control by PI PI controller has two components. These components are named as Proportional (
)
and Integral ( ) and each are expressed a coefficient. In PI controller, output of the system is brought about to desired value, setting appropriate
and coefficients.
Mathematical model of the PI controller is as shown.
∫
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2.3.4
Fuzzy Logic Control
Fuzzy logic is a design philosophy which deviates from all the previous control methods by accommodating expert knowledge in controller design. FLC is one of the most successful applications of, fuzzy set theory. Its major features are the use of linguistic variables rather than numerical variables. Linguistic variables, defined as variables whose values are sentences in a natural language (such as small and large), may be represented by fuzzy sets. Fuzzy set is an extension of a crisp set, where an element can only belong to a set (full membership) or not belong at all (no membership). Fuzzy sets allow partial membership,which means that an element may partially belong to more than one set. FLC‟s are an attractive choice when precise mathematical formulations are not possible (Mattavelli et al.,).
Figure 2.13 Basic Configuration of FLC
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The general structure of an FLC is represented in Figure 2.13 and comprises four principal components: 1) a fuzzification interface which converts input data into suitable linguistic values; 2) a knowledge base which consists of a data base with the necessary linguistic definitions and control rule set; 3) a decision making logic which, simulating a human decision process, infers the fuzzy control action from the knowledge of the control rules and the linguistic variable definitions; and 4) a Defuzzification interface which yields a nonfuzzy control action from an inferred fuzzy control action. It is adaptive in nature and can also exhibit increased reliability, robustness in the face of changing circuit parameters, saturation effects and external disturbances and so on (Govindaraj et al., 2011).
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PROJECT BLOCK DIAGRAM DESCRIPTION
Fuzifier
This is the first step done in a fuzzy logic. It converts the measured signal X (which might be the error signal in a control system) into a set of fuzzy variables. It is done by giving values (there will be our fuzzy variables) to each of a set of membership functions,. The values for each membership function are labeled u(x), and are
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determined by the original measured signal X and the shapes of the membership functions. Decision making
Fuzzy control uses fuzzy equivalents of logical AND, OR and NOT operations to build up fuzzy logic rules. Fuzzy control rules are obtained from the analysis of the system behavior. In the formulation it must be considered that the converter performances in terms of dynamic response and robustness. Defuzzification
This is the last step in building a fuzzy logic system where the fuzzy variables generated by the fuzzy logic rules are turned into a real signal again. It combines the fuzzy variables to give a corresponding real (crisp or non-fuzzy) signal which can then be used to perform some action. on 3/10/2011).
Gantt chart
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(control-systems-principals.co.uk, accessed
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Public University of Navarra, Department of Electrical and Electronic Engineering, Pamplona, Spain
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