DSP based proportional integral sliding mode controller for photo-voltaic system

Electrical Power and Energy Systems 71 (2015) 123–130

Contents lists available at ScienceDirect

Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

DSP based proportional integral sliding mode controller for photo-voltaic system Subramanya Bhat a,⇑, H.N. Nagaraja b a b

Department of E&C, Canara Engineering College, Mangalore, VTU, Belgaum, India Indus University, Ahmedabad, India

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 12 June 2014 Received in revised form 11 February 2015 Accepted 20 February 2015 Available online 16 March 2015

The buck–boost converter is controlled using different algorithms like voltage mode control, current mode control, V2 control, enhanced V2 control, Sliding Mode Control (SMC), and Proportional Integral (PI) control. In all these algorithms the steady state error is more. On combining PI control and sliding mode control the steady error can be minimized. In industry and commercial applications involving Photo-Voltaic (PV) systems, uses buck–boost converter. In this converter above control algorithms are implemented using hardware circuitry or microcontroller. In industry and commercial applications Digital Signal Processor (DSP) is used for automation purposes and the same DSP can be used to implement control algorithms so as to get maximum electrical energy from solar energy. The efficient utilization of resources such as DSP is achieved as we are using the same DSP for implementing control algorithm. In the proposed study, PI control method and sliding mode control methods are combined to obtain a Proportional Integral Sliding Mode Control (PISMC) and it is used to control the buck–boost converter which is used to drive the electrical loads from solar energy. The buck–boost converter is designed, simulated and implemented. The algorithms PI, SMC and PISMC are simulated in using MATLAB simulink and then implemented in DSP TMS 320 2808. In the proposed study PISMC, a stable and efficient output voltage is obtained in which the steady state error and maximum overshoot are minimum. The PISMC is better in terms of transient and steady state performances as validated by our experiments. The proposed study will work in real-time since DSP is used for implementing the control algorithms and found to be better in terms of speed and regulation. The proposed DSP based PISMC can also be used to control other types of DC–DC converters. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Steady state error Control algorithm DC loads Regulation

Introduction In a large number of industrial, commercial and residential applications it is required to convert a fixed DC voltage to a different DC voltage level with a regulated output. To perform this task a DC–DC converter is needed. A DC–DC converter converts a DC voltage of one level to another. In the proposed work a DC to DC converter called buck–boost converter is used to drive electrical loads from solar panel input. In industry and commercial applications Digital Signal Processor (DSP) is used for automation purposes and the same DSP can be used to implement control algorithms so as to get maximum electrical energy from solar energy. The DSP is more accurate and it will work in real time. In Industry and commercial applications involving automation using DSP is ⇑ Corresponding author. E-mail addresses: [email protected] (H.N. Nagaraja).

(S.

Bhat),

http://dx.doi.org/10.1016/j.ijepes.2015.02.038 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

[email protected]

underutilized. Hence in the proposed study, the DSP which is used for automation process is used for implementing control algorithms. Photovoltaic generation is reliable and its operation and maintenance cost is low. The PV system also provides social and economical benefits to the society where other forms of electricity are unavailable. The buck–boost converter is used for charging the battery from solar module. In PV power generation system, other than solar modules, many circuits and devices are required to provide a satisfactory electricity supply. Many systems implemented in the literature [1–4] have a provision for energy storage to supply electricity at night and during cloudy weather. In these papers, they have mentioned about different types of battery storage systems. In order to control the energy generated from the solar cell the various power conditioning and control circuits are needed. A microcontroller based stand alone PV system described in [5], uses low cost microcontrollers to control the switching period of the switch used in converter and inverter. In this work, the output waveforms have unexpected even harmonics which is due to the

124

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

low clock speed, microcontroller approximates switching angles instead of accurate values. The DSPs have more computational power than microcontrollers. Hence more advanced control algorithms can be implemented on a DSP. In the proposed method, PISMC is implemented on a DSP TMS320 2808. PI controllers are linear controllers in which steady state error is more. Sliding mode controllers are non linear controllers in which the steady error is less. Hence in the proposed method PI controllers are combined with sliding mode controllers to achieve better control. The sliding mode controllers have good robustness properties. The sliding mode control of DC–DC converters are well discussed in [6–10]. The disadvantages with sliding mode controllers are that they are sensitive to noise and they operate at variable switching frequency which limits the selection of inductor. The implementation of PI controller discussed in [10] is subjected to external disturbances. This can be overcome by adaptive sliding mode control. The methodology of the proposed study is discussed in Section ‘Methodology’. The PI, SMC and the proposed study PISMC are tested and the results are presented in Section ‘Results’. The results are discussed in Section ‘Discussion’. The proposed study is concluded in Section ‘Conclusion’. Methodology The block diagram of proposed study is shown in Fig. 1. The voltage from solar panel is taken as input to the buck–boost converter. The output of buck–boost converter is stored in battery which is used to drive DC loads LED lamp, modem and fan. The buck–boost converter is designed, simulated and implemented. The load voltage and current are sensed and compared with the reference signal and the output of the same is given to ADC. The ADC converts analog value to digital and this output is given to the digital PISMC. The PISMC control algorithm is implemented using a DSP. The DSP will generate PWM wave and it is used to trigger the MOSFET switch in buck–boost converter. The advantage of this DSP is that it can generate PWM wave in real-time [12,13]. The amplitude of PWM wave generated from DSP is more than 3 V and frequency is 50 kHz. Hence, gate drive circuit is not necessary for the proposed study. But Akkaya and Kulaksiz [5] used micro controller for solar PV system which generates PWM wave, the amplitude is less to trigger the switch in buck–boost converter. Hence they used gate driver circuit to increase the amplitude of PWM wave. Because of gate driver circuit the power consumption is increased and size and cost of the system will also be increased.

Input voltage from solar Panel

Mathematical modeling The solar panel is modeled mathematically as follows. The PV generator is formed by connecting many PV cells in series and parallel to get the desired output voltage and current [1]. The PV generator shows a nonlinear V–I characteristics. The V–I characteristics with Ns cells in series and Np cells in parallel is given by Eq. (1)



Ns Np

V g ¼ Ig Rs

 þ

     Ns Iph  Ig Ns ln 1 þ D N p Io

where D = q/AKT where q = electric charge of an electron, A = completion factor, K = Boltzman constant, T = absolute temperature, Io = cell reverse saturation current, Ns = number of cells in series, Np = number of cells in parallel, Iph = insolation dependent photo current, Ig = solar cell array current, Vg = solar cell array voltage. The equivalent circuit is shown in Fig. 2. Here Rs is the series resistance and Rsh is the parallel resistance of cell. We developed a mathematical model for the buck–boost converter used in PV system. The mathematical model is developed using state space equations in the following. The structure of buck–boost converter is shown in Fig. 3. The output voltage of buck–boost converter is more or less than the input voltage which depends on duty ratio of the switch. The switch is implemented using MOSFET. The equations for buck–boost converter using state space averaging method is obtained as follows. When the switch is ON, the state space equations are obtained as dIL ¼  VLin dt dV c 1 ¼  RC dt

) ð2Þ

vo

When the switch is OFF, the state space equations are written as dIL ¼  vLo dt dV c 1 ¼  RC dt

) ð3Þ

v o  IC

L

The state space representation for ON mode is given by

x_ ¼ A1 x þ B1 u

 ð4Þ

V c ¼ C1x where A1 ¼



0 1=C

1=L 1=RC



B1 ¼

  0 C 1 ðxÞ ¼ ½ 0 0

DC Load (LED Lamp ,Modem & Fan)

Buck-Boost Converter Baery

Current Sensor circuit

PWM generaon with DSP TMS 320 2808

ð1Þ

Voltage Sensor circuit

Reference Signal

Comparator

Fig. 1. Block diagram of the proposed method.

Error Amplifier

1  and u ¼ V in .

125

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130 Table 1 The load ratings. Device

Power rating (W)

Output voltage (V)

Current (A)

Tube light Fan Modem

7 16.8 5.5

12 12 10

0.58 1.4 0.55

Switching frequency of the switch is taken as f = 50 kHz,

Fig. 2. Equivalent circuit of solar panel.

Lcr ¼

Vg  D f  DiL

ð14Þ

Using Eq. (14) we will get the inductor value as L = 1.15 mH

C cr ¼

Dio  D f  DV o

ð15Þ

The output voltage ripple is taken as DV o ¼ 1% of output voltage. Using Eq. (15) the capacitor value is obtained as 220 lF. Fig. 3. Buck–boost converter structure.

PI control of buck–boost converters

The state space representation for OFF mode is given by

x_ ¼ A2 x þ B2 u

 ð5Þ

V c ¼ C2x

   0 0 1=L B2 ¼ C 2 ¼ ½ 0 1  and u ¼ V in . 0 1=RC 0 The averaged state space representation of buck–boost converter system is obtained and represented by the following equations: where A2 ¼



x_ ¼ ½aA1 þ ð1  dÞA_ 2 x þ ½dB1 þ ð1  dÞB2 v in

)

ð6Þ

Vc ¼ ½dC 1 þ ð1  dÞC 2 x

where d is the duty ratio of the MOSFET. IL is the inductor current and Vc is the voltage across the capacitor and R is the load resistance. From system point of view, d is the control input, E is the voltage and R is the output resistance. In matrix form the Eqs. (2), (4) and (6) is written as

"

I_L V_ c

#

" ¼

0  1d L

1d L 1  RC

#



IL Vc

 þ

d=L 0



v in

ð7Þ

For the state space model the state space variables chosen are; inductor current x1 = IL and capacitor voltage x2 = Vc. Output of the model is taken as capacitor voltage y = x2. The simple form of Eqn.(7) is as follows

x_ ¼ Ax þ Bu

ð8Þ "

Where the system parameter matrix is A ¼

State dependent input matrix as B ¼  And the state matrix is x ¼

IL



d=L 0

0  1d L

1d L 1  RC

#

 ð10Þ

ð11Þ

The buck–boost converter is designed as follows. Load specifications are taken as follows (see Table 1). Total load current is obtained as 2.53 A. Output voltage of a buck–boost converter is given by,

Vo ¼ Vi

D 1D

We took;

ð12Þ

DiL ¼ 3%IL

where IL ¼

Io 1D

uðtÞ ¼ K p  eðtÞ

ð16Þ

where Kp is the proportional gain e(t) is the error and u(t) is the perturbation in output signal of PI controller from the base value corresponding to normal operating conditions. It with no integration property always exhibit static error in the presence of disturbances and changes in set-point and shows a relatively maximum overshoot and long settling time. To remove steady-state offset in controlled variable of a process, an extra intelligence is added to the P controller and this intelligence is the integral action. The controller is a PI controller whose mathematical notation is depicted in Eq. (17)

  Z t uðtÞ ¼ K c eðtÞ þ 1=K i eðtÞdt

ð17Þ

0

The simulink diagram for PI control of buck–boost converter is shown in Fig. 4. In this figure output voltage of converter is compared with a reference source of 12 V and the error signal generated is applied to PI controller. The PI controller output is compared or ANDED with a pulse generator output to obtain PWM wave so as to trigger the MOSFET switch. Sliding mode control of buck–boost converters

ð9Þ



VC

A PI controller fuses the properties of P and I controllers and the algorithm provides a balance of complexity and capability to be widely used in process control applications. It is reported that single input single-output PI controller controls 98% of control loop in paper and pulp industries. Eq. (16) describes P controller.

ð13Þ

In SMC, a controller is forcing the system states to reach, and remain on, a predefined switching surface within the state space. This motion to a predefined switching surface is known as sliding motion. The advantages of this type of motion or control are reduction in system order and control is insensitive to parameter variations. Due to these advantages, the buck–boost converter is controlled using SMC. The buck–boost converter output voltage error and rate of change of voltage are both selected as state variables. The SMC is implemented using two control loops and they are inner current loop and the outer voltage loop as shown in Fig. 5. These two loops are combined in series to achieve SMC for buck–boost converter. The equations used in SMC are explained as follows. Let us consider voltage error as X, rate of change of voltage error as Y and integral of voltage error as Z. Under continuous conduction mode we can write as derived in [11]

X ¼ ðV ref  bV o Þ

ð18Þ

126

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

Fig. 4. Simulink diagram for PI control of buck–boost converters.

Y ¼ X_ ¼ b=C

Z¼

Z



vo

RL



Z

1½uV i  V o  dt RL



Xdt

ð20Þ 2

X buck-boost

ð19Þ

3

ðV ref  bV o Þ h i 6 v o R 1½uV i V o  dt 7 7 ¼6 RL 4 b=C RL  5 R ðV ref  bV o Þdt

X_ buck-boost ¼ AX buck-boost þ BU 2

0  6 .. . . 6. . Where A ¼ 6 6 40 

1 .. . 1 R1 C

1 ... 2

0

3 0 .. 7 .7 7 7 05

ð21Þ

ð22Þ

ð23Þ

where s is the instantaneous state variable trajectory and is described as

s ¼ a1X1 þ a2X2 þ a3X3 ¼ J T X

ð26Þ

where JT ¼ ½/ 1 / 2 / 3. Where / 1; / 2 and / 3 represents control parameters and these are known as sliding coefficients. A sliding surface is obtained by substituting S = 0. The mapping of the equivalent control function on the duty ratio control d is done as follows.

0
Vc <1 V ramp

This gives the following relationship for the control signal Vc and ramp signal Vramp, where

V C ¼ U equ ¼ bL½ð/ 1= / 2Þ  ð1=R1 CÞic þ LCð/ 3= / 2ÞðV ref  bV o Þ

0

þ bðV o  V i Þ

ð27Þ

3

0 6 bV o 7 B ¼ 4 LC  bV i =LC 5 0

ð24Þ

V c ¼ K p1 ic þ K p2 ðV ref  bV o Þ þ bðV o  V i Þ

ð28Þ

where

For the buck–boost converter the sliding mode control adopts a switching function such as

K p1 ¼

      /1 1 /3  &K p2 ¼ LC /2 R1C /2

ð29Þ

u ¼ 1 when S > 0 V ramp ¼ bðV o  V i Þ

u ¼ 0 when S < 0 where u ¼

1 2ð1 þ sgn sÞ

ð25Þ

ð30Þ

Eqs. (27) and (30) are derived using Eq. (26) and the mapping of the equivalent control function on duty ratio control d. Using these equations the SMC for buck–boost converter is modeled as shown

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

127

Fig. 5. Model of sliding mode control algorithm.

in Fig. 5. The capacitor current ic is measured and multiplied with a constant Kp1. The output voltage is measured from a voltage divider circuit to get bVo, where b = R2/(R1 + R2). The voltage bVo is compared with reference voltage Vref, the output of which is multiplied with a constant Kp2. The input voltage is also multiplied with b and compared with bVo. The outputs Kp1ic, b(Vo  Vi) and Kp2x1 are added to get a signal Vc. Using comparator, output signal Vc and ramp signal Vramp are compared to get PWM signal to trigger the MOSFET switch in a buck–boost converter. The model developed for sliding mode control algorithm is implemented using simulink diagram as shown in Fig. 6. The ADD blocks and Gain blocks from simulink library are used for comparators and multipliers respectively. The relay switch and pulse generators are used to generate a PWM wave. Proportional integral sliding mode control of buck–boost converters In the proposed study PISMC is simulated first and then implemented on a DSP TMS 2808. In this control algorithm the advantages of PI control and sliding mode control methods are combined. The simulation diagram for the same is shown in Fig. 7. For developing the simulation diagram the equations and models derived in Sections ‘PI control of buck–boost converters’ and ‘Sliding mode control of buck–boost converters’ are used. The output of PI controller is applied as input to sliding mode controller to obtain a PWM wave. The advantage of PISMC is that the steady state error and maximum overshoot are minimized.

Results The simulation outputs with PI, SMC and PISMC are shown in Figs. 8–10 respectively. The comparison of control algorithms with respect to maximum overshoot, rise time, settling time and steady state error is done. The comparison is tabulated in Table 2. It has been found from Figs. 8–10 and Table 2 that the proposed PISMC has less maximum overshoot and steady state error compared to other controllers. In all the three controllers overshoot has been found which is due to transient state of the controller. As the steady state is reached the expected output voltage of 12 V is achieved in all the three controllers. But steady state error and maximum overshoot are more in PI and SMC controllers. For buck–boost converter used in PV systems these parameters must be minimum as possible. In the proposed PISMC these parameters are drastically reduced as found in Figs. 8–10 and Table 2. In proposed PISMC there is a small increase in rise time and settling time but these parameters significance on buck–boost converter performance is minimum. The experimental set up is shown in Fig. 11. The solar panel is connected to buck–boost converter. The buck–boost converter output is given to battery which drives DC loads such as DC LED lamp, DC fan and modem. The solar panel is manually adjusted to receive maximum solar radiation. The control algorithm is implemented on a DSP as shown in Fig. 12. The output voltage and current are measured and given to comparators. The advantage of TMS 320 2808 is that it has in built ADC and eight PWM generators. The comparator output is given to DSP. The DSP is generating a PWM

128

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

Fig. 6. Simulink diagram for sliding mode control of buck boost converters.

Fig. 7. Simulink diagram for PI SMC control of buck boost converters.

wave based on PISMC of amplitude more than 3 V and frequency 50 kHz. The electrical characteristics of the panel are tabulated in Table 3. These characteristics are considered while designing buck–boost converter for solar panel.

Discussion In industry and commercial applications with PV system uses hardware circuit or microcontroller to get good regulation and

129

Load Voltage (Volts)

Load Voltage (Volts)

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

Time (sec) Fig. 8. PI controller output.

Time (sec) Fig. 10. PI SMC controller output.

Load Voltage (Volts)

Table 2 Comparison of control algorithms. Type of controller

Rise time in ms

Maximum overshoot in %

Settling time in seconds

Steady state error in %

PI SMC PISMC

1.77 1.66 2.27

22.08 22.92 19.91

0.0189 0.01348 0.02255

2.33 2 1.00

Time (sec) Fig. 9. SMC controller output.

speed [14,15]. The cost, accuracy and speed of hardware circuitry or microcontroller is less when compared to DSP. They used dedicated hardware circuitry or microcontroller to get the control action. In Industries and commercial application uses DSP for automation purposes. The same DSP if it is used for implementing control algorithms, we can achieve the efficient utilization of the resource. The speed and regulation will be better. Even though initial cost of DSP is high, as we are converting solar energy to electrical energy we get more efficiency over the years. In rural areas where other forms electricity are unavailable PV system plays an important role. In rural villages for residential applications if the PV systems controlled with DSP, we can achieve good regulation and efficiency. The proposed PISMC algorithm is useful due to high performance and simple implementation. It is seen that the PISMC controller meets our demand of controlling the output voltage of buck–boost converter in a smooth manner without much more chattering in the transient period by decreasing the rate of transition between the states of high frequency oscillation and low frequency steady state value and thereby shows a sharp decrease in rise time and settling time. The implementation of PISMC controller also reduces maximum overshoot and thereby reduces the chances of damage due to sudden rise of voltage in modern day

Fig. 11. Experimental set up: solar panel.

power electronic devices having a very narrow tolerance zone to meet the requirements ultrafast performance. In proposed study, PISMC is implemented on a DSP. The buck–boost converter is designed for PV system, simulated in MATLAB simulink and then implemented using hardware and DSP. The efficient utilization of resources such as DSP in industry and commercial applications is addressed in the proposed study. The PI and SMC algorithms are combined to get PISMC which gives better transient and steady state performances as validated by our experiments. Bhat and Nagaraja in [20] developed a novel DSP based boost converter. PID control algorithm was implemented in DSP TMS 6713. The DSP processor is used in the feedback path and good regulation was achieved. But the drawback is that the DSP here able to

130

S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130

be used with a good control algorithm. In industries and commercial applications involving automation process with DSP, the resources such as DSP is underutilized. In rural villages, where there are other forms of electricity unavailable, solar energy is most promising one. The cost of DSP processor is reducing and its computational power is increasing during the last decade. Hence DSP processor can be used to implement control algorithms when compared to microcontroller and hardware circuitry. To address the above issues a reliable DSP based PISMC is developed in the proposed study. In the proposed study, the buck–boost converter for PV system is designed, simulated and implemented. The control algorithms such as PI control, SMC control and PI SMC control are implemented on a DSP processor. It was found that PISMC has less steady state error and less maximum overshoot. The proposed study DSP based PISMC for PV system provides improved line and load regulations. The proposed work is better in terms of speed, accuracy, regulation and cost.

Fig. 12. DSP interfacing with solar panel.

References

Table 3 Electrical characteristics of the panel. Std. temperature Mean irradiance Module temperature Module area Cells in series ISC Imp Pmax Cell efficiency Shunt resistance Cell area Cells in parallel Measurements in radians VOC Vmp Fill factor Module efficiency Series resistance

25 °C 1.000 kW/m2 25.4 °C 4094.24 cm2 36 2.96 A 2.68 A 48.611 W 16% 519.79 X 84.2 cm2 1 1.000 kW/m2 22.579 V 18.128 V 72.8% 11.9% 0.923 X

produce a waveform of a maximum 8 kHz frequency and an amplitude of 2 V. But for triggering the MOSFET it needs a PWM signal of 20 kHz and 8 V. Additional circuits are developed to get a PWM signal of 20 kHz and 8 V and hence the system became bulky. Bhat and Nagaraja in [21] developed a novel DSP based buck boost converter. Here a buck–boost converter is simulated and interfaced to DSP TMS320C2808. The interfacing with DSP is discussed in detail. DSP TMS320C2808 is having more computational power and accuracy as compared to microcontrollers and other DSP’s [18,19]. The PWM waveform of 50 kHz is generated from DSP. In proposed work DSP TMS320C2808 is interfaced to buck–boost converter. The work is superior because the input is taken from solar panel, energy is stored in battery. Non conventional energy i.e. solar energy is stored in a battery and then it is used to drive DC loads. In the proposed work better transient and steady state performances such as maximum overshoot and settling time is achieved by implementing PISMC control algorithm in DSP. Now, DSP processors are becoming cheap with more computational power as compared to microcontrollers [16,17]. Hence the proposed system has more practical significance. The work can be further enhanced to increase the load capacity. Conclusion The solar energy is abundantly available in nature and this should be used as an alternative to conventional energy sources. For the efficient use of solar energy a buck–boost converter should

[1] Su W, Huang S, Lin C. Economic analysis for demand-side hybrid photovoltaic and battery energy storage systems. IEEE Trans Ind Appl 2001;37(1). [2] Cook GM, Spindler WC, Grefe G. Overview of battery power regulation and storage. IEEE Trans Energy Convers 1991;6:204–11. [3] Harrington S, Dunlop J. Battery-charge controller characteristics of photovoltaic systems. IEEE AES Mag 1992(8). [4] Kulaksız AA. The control of electrical energy (with power electronic systems) which is obtained from photovoltaic module. MSc dissertation, Selcuk Universitesi, Fen Bilimleri Enstitusu, Konya, Turkey; 2001. [5] Akkaya R, Kulaksiz AA. A microcontroller based stand-alone photovoltaic power system for residential appliances. Appl Energy 2004:419–31. Elsevier. [6] Rafiq M, Rehman S, Rehman F, Butt Q. Performance comparison of pi and sliding mode for speed control applications of SR motor. Eur J Sci Res 2011;55:363–80. [7] Lai Y, Tan S, Wu C. Design of a PWM based sliding mode controlled buck-boost converter in continuous-conduction-mode. ECTI Trans Electr Eng Electron Commun 2007;5:129–33. [8] Ahmed M, Kuisma M, Pyrhonen O, Silventoinen P. Sliding mode control for buck-boost converter using control desk dSPACE. In: The fifth international conference on power electronics and drive systems; 2003. p 1491–4. [9] Fadil H, Giri F. Reducing chattering phenomenon in sliding mode control of buck-boost power converters. IEEE Int Sympos Ind Electr 2008;5:287–92. [10] Alvarez J, Cervantes I, Espinosa G, Maya P, Morales A. A stable design of PI control for DC–DC converters. IEEE Trans Circ Syst I: Fundam Theor Appl 1991:103–6. [11] Tan SC, Lai YM, Tse CK. Design of a PWM based sliding mode controlled buck boost converter in continuous conduction mode. In: Proceedings of 11th European conference on power electronics and applications (EPE-2005); September 2005. [12] Toliyat Hamid A, Campbell Steven G. DSP-based electromechanical motion control. CRC Press; 2003. [13] Guo L, Hung JY, Nelms RM. Digital controller design for buck and boost converters using root locus techniques. In: The 29th annual conference of the IEEE industrial electronics society (IECON’03), vol. 2; November 2003. p. 1864– 9. [14] Oliva Alejandro R, Ang Simon S, Bortolotto Gustavo Eduardo. Digital control of a voltage mode synchronous buck converter. IEEE Trans Power Electron 2006;21(1). [15] Peretz Mor Mordechai, Ben Yaakov Shmuel. Time domain design of digital compensators for PWM DC–DC converters. IEEE Trans Power Electron 2012;27(1). [16] Guo Liping, Hung John Y, Nelms RM. Evaluation of DSP based PID and fuzzy controllers for DC–DC converters. IEEE Trans Industr Electron 2009;56(6). [17] Zhen Z, Milan M. Implementation and performance evaluation of DSP based control for constant frequency discontinuous conduction mode boost PFC front end. IEEE Trans Industr Electron 2005;52(1). [18] Bose BK, Szczesny PM, Steigerward RL. Microcomputer control of a residential photovoltaic-power conditioning system. IEEE Trans Ind Appl 1985;IA20:1182–91. [19] Eltawil Mohamed A, Zhao Zhengming. MPPT techniques for photovoltaic applications. Renew Sustain Energy Rev 2013;25:793–813. Springer. [20] Bhat Subramanya, Nagaraja HN. A novel DSP based boost converter. In: CSIR sponsored  control instrumentation system conference CISCON 2013, Manipal, Bonfring Publishers; December 2013. p 78–81. [21] Bhat Subramanya, Nagaraja HN. A novel DSP based buck boost converter. In: National conference on emerging trends in engineering, technology and management, Ahmedabad, India; February 2014. p. 319–21.