State Space Analysis and Design of Forward Converter System by Using a Gilbert’s method of Tuning for the Controllability and Observability

ABSTRACT

State space analysis using a gilberts method of tuning the controller in forward converter system is discussed in this paper. High constant voltage during variation, isolation during high frequency switching, derivative of the transient response, conversion occurs with high switching frequency, reduced noises from ripples and the range of steady state are all required necessities for the forward converter. In this paper, a state space analysis with high frequency switching is proposed and it is used for the forward converter system to obtain the controllability and observability which is tuning by gilberts method for charging a battery of a server SMPS system is proposed. In this paper, the state space analysis which is formulated in vector form and it is tuned by the first order derivative differential equation, as formulated by gilberts. With this circuit topology, soft high frequency switching occurs during conversion and reduces the switching loss and also it produces the desired voltage for the system. The conventional forward converter and the modified forward converter system using state space method are simulated using Matlab-Simulink and the comparison has been done from the two converters are described and the simulation results are presented, which is to find the appropriate circuit for the server SMPS system. Keywords: State space analysis, Gilberts transforms, High switching frequency, Controllability, Observability.

INTRODUCTION

In recent years, the switching mode power supply (SMPS) system which produces the variable voltage or fixed level of voltage been achieved with high density power and high enactments by using the power semiconductor devices such as IGBT, MOS-FET and SiC. However, by using the switching power semiconductor devices in the SMPS system, the problematic of the switching loss and the interference noises such as EMI/RF has been closed up. By the direction of the International Special Committee on Radio Interference (CISPR) and the EMC limitation of harmonics for the International standard is Electro technical Commission (IEC). As by the limitation and directions, the noise filter must add to the SMPS system, for the EMI/RFI noises must add metal and magnetic component shield and for the input harmonic current must add large input filter to the PFC converter circuit. The high frequency switching operation can achieve in the SMPS system by the development of power semiconductor device technology, but the switching losses have occurred. For the high frequency switching the size of cooling fan could be huge because of the increase of switching losses, and also the inductor and transformer size has been reduced.

LITERATURE REVIEW

Our research target is to maintain the fixed voltage level and to reduce the ripple and switching losses during conversion in the SMPS system. One method is the soft switching technique and the other method is by proper choosing of proper tuning with controller circuit. This technique can minimize the switching power losses of the power semiconductor devices, and reduce their electrical dynamic and peak stresses, voltage and current surge-related EMI/RFI noises under high frequency switching strategy. This paper proposes a new DC to DC forward converter topology for PV applications. Its operating principle, static characteristics, comparison analysis between the proposed converter and the Non-Inverting Buck-Boost converter is carried out for three different scenarios are studied. The proposed converter provides higher efficiency than the NIBB converter is presented [1]. An appropriate topology of a ZVS based Phase Shifted full -bridge DC-DC converter is selected based on advantages of reduced switching losses and stresses with fixed switching frequency. A feed forward voltage mode control is utilized which is easier to design and analyze with good noise margin and stable modulation process and improved line regulation are given [2]. This study presents the analysis and design of a novel technique that improves the efficiency of the conventional forward DC-DC converter by reducing switching losses, along with a comprehensive analysis of the circuit and detailed information for designers. A 5 kW step-down prototype is presented [3]. The auxiliary circuit has only passive elements and thus, the control circuit is simple and is like a regular PWM DC-DC converter. The auxiliary circuit provides ZVS condition for primary switch at turn-off instances. A new soft switching forward-fly-back DC-DC converter is proposed [4]. A double-sided LCLC-compensated capacitive structure dramatically reduce the voltage stress in the capacitive power transfer (CPT) system is proposed for the electric vehicle charging applications with improved efficiency are given [5]. The method to step up the voltage gain by reducing the conduction and switching losses are presented [6]. A closed loop model is proposed for the critical applications and the methods to improve the quality by reducing the error are presented [7]. Due to the comparison from the converters, the simulation results of the double forward converter gives better performance is proposed [8]. Comparison between the converters with constant source and with constant load, which is used to check the maximum power transfer to the load is also presented [9]. The new step up and step down method of switching is used to reduce the stress and the comparison between the simulation and experimental results is also presented [10]. The above literature does not deal with the design and analysis of forward converter using the state space method with gilberts formulation for tuning the circuit. The above cited papers do not deal with the comparison of converters which is conventional forward converter in state space and the modified forward converter with gilberts tuning in state space method and do not identify a converter circuit suitable for SMPS system. This work aims to develop simulink models for the above forward converter system. A comparison is also done to find the circuit suitable for the SMPS system and the simulation results are presented.

STATE SPACE SYSTEM FOR THE FORWARD CONVERTER

This section introduces the proposed state space model for the forward converter which is illustrated in Figure 1. In the state space formulation, for the dynamic system with a minimum restrictions of state variables which can be defined these variables when t=t0. If t>t0, it completely determines the behavior of the system. The system represents all the state and it can be notified as m-inputs, p-outputs and the n-state variables. Figure 1 State space system for the forward converter. Figure 2 Closed loop state space system for the forward converter. The state space model for the closed loop controlled forward converter which is illustrated in Figure 2. Let, the state variables are represented as x1(t), x2(t), x3(t)......xn (t), the input variables are represented as u1 (t), u2 (t), u3 (t)......um (t) and the output variables are represented as y1 (t), y2 (t), y3 (t)......yp (t). These variables such as input variables, output variables and state variables are represent in the vector form which denotes only the magnitude as well as the direction. The state space model approach can be functional for any type of system, but the analysis can be carried on multiple input and output systems with the initial conditions. The state space model approach is a powerful tool with the technique for the design, analysis and tuning of the control system. These three variables which are input variables, output variables and state variables are present in the vector form, that can be derivate with first order differential equations and it can be arranged in the n-form of derivation. Derivate with differential equations and it can be in the n-form, which can be written in a vector form. For a linear time invariant systems, the first derivative of state variables can be expressed as a linear combination which is to satisfy the superposition principle, the state variables and input variables are combined as a derivative of state model. For a linear time invariant systems, the first derivative of output variables can be expressed as a linear combination which is to satisfy the superposition principle, the state variables and input variables are combined as a derivative of the output of state model. From eq. (6), the derivatives can be represented as Ẋ(t) =A X(t) +B U(t)]-------------(8). Where, the state vector X (t) is in the order of (n*1), the input vector U (t) is in the order of (m*1), system matrix A is in order of (n*n) and input matrix B is in the order of (n*m). Similarly from eq. (7), the derivatives can be represented as the response of the system Y (t), Y (t) =C X (t) +D U (t)]-------------(9) Where, the state vector X (t) is in the order of (n*1), the input vector U (t) is in the order of (m*1), the output vector Y(t) is in the order of (p*1), transition matrix D is in order of (p*m) and output matrix C is in the order of (p*n). The eq.(8) represent the state equation and the eq.(9) represent the output equation which together combines to form a state model of the linear time invariant system. Ẋ (t) =A X (t) +B U (t)]------------state equation and Y (t) =C X (t) +D U (t)]-----------output equation. From the state equation and the output equation, the block diagram which is represented in the closed loop model as in Figure 2. This section introduces the parameters assumption by tuning the system for the forward converter which is illustrated in Figure 3. It constitutes the state vector x1, x2 and x3 for tuning as by the gilberts rule and to check the system whether it is in controllable or it is in observable. From figure 3, X1(s) =[X2(s)-X3(s)] [2/[s(s+1)]], X3(s) =Sx1(s) and X2(s) = [U(s)-X1(s)] [2/s+3]. By taking the inverse Laplace transforms for the above given equations and rearrange the equations, we get ẋ1=x3----------------------------(10) ẋ2= -2x1-3x2+2u---------------(11) ẋ3=2x2-3x3---------------------(12) y=x1------------------------------(13) By using the equ.10 to equ.13, where ẋ1=x3, ẋ2= -2x1-3x2+2u, ẋ3=2x2-3x3 and the output equation y=x1 are used to tuning the circuit as by the gilberts rule. The values are used in the vector form which is tunable. The values for the state model as by the gilberts rule are in the vector, which represented as A [0 0 1; -2 -3 0; 0 2 -3], vector B [0 2 0] and vector C [1 0 0], which are represented in Figure 4 as parameters.

SIMULATION RESULTS

The SMPS system is modeled and simulated using the blocks of MATLAB SIMULINK. The SMPS system using conventional forward converters and the modified forward converter using state space method controller are simulated and the results are presented. The conventional forward converter is shown in Figure 6.1. DC output voltage is shown in Figure 6.2. The open loop controlled conventional forward converter is shown in Figure 6.3. DC input voltage and output voltage with disturbance are shown in Figure 6.4 and Figure 6.5. The closed loop controlled conventional forward converter using state space model is shown in Figure 6.6. DC input voltage and output voltage with disturbance are shown in Figure 6.7 and Figure 6.8. The open loop modified forward converter is shown in Figure 6.9. DC input voltage and output voltage with disturbance are shown in Figure 6.10 and Figure 6.11. The closed loop controlled modified forward converter is shown in Figure 6.12. DC input voltage and output voltage with disturbance are shown in Figure 6.13 and Figure 6.14. The closed loop controlled modified forward converter using fuzzy logic controller is shown in Figure 6.15. DC input voltage and output voltage with disturbance are shown in Figure 6.16 and Figure 6.17. The closed loop controlled modified forward converter using Ann logic controller is shown in Figure 6.18. DC input voltage and output voltage with disturbance are shown in Figure 6.19 and Figure 6.20. The modified forward converter using state space analysis and tuned by the method gilberts is shown in Figure 6.21. By using the gilberts rule are in the vector, which represented as A [0 0 1; -2 -3 0; 0 2 -3], vector B [0 2 0] , C [1 0 0], and the vector D is not defined, but literally an initial value of 0.02 is applied, which are simulated by using the given parameters which is illustrated in this Figure. DC input voltage and output voltages with disturbance are shown in Figure 6.22 and Figure 6.23 and the results are presented. Figure 6.1 Simulink model of a conventional forward converter. Figure 6.2 DC output voltages across the load. Figure 6.3 Open loop controlled conventional circuit. Figure 6.4 DC input voltage with disturbance. Figure 6.5 DC output voltages across the load. Figure 6.6 Closed loop controlled circuit using state space model. Figure 6.7 DC input voltage with disturbance. Figure 6.8 DC output voltages across the load with ripples. Figure 6.9 Open loop controlled modified converter. Figure 6.10 DC input voltage with step change. Figure 6.11 DC output voltage with step change. Figure 6.12 Closed loop controlled modified converter. Figure 6.13 DC input voltage with step change. Figure 6.14 DC output voltage with step change. Figure 6.15 Closed loop controlled modified converter using fuzzy logic. Figure 6.16 DC input voltage with step change. Figure 6.17 DC output voltage with step change. Figure 6.18 Closed loop controlled modified converter using ANN controller. Figure 6.19 DC input voltage with step change. Figure 6.20 DC output voltage with step change. Figure 6.21 Closed loop controlled modified converter using state space model. Figure 6.22 DC input voltage with step change. Figure 6.23 DC output voltage tuned with step change. The output voltage with reduced ripple is shown in Figure 6.23. Summary of steady state error is shown in Table 1. Summary of time-domain specifications and steady state error are given in Table 2. Summary of transient response and its range of steady state are given in Table 3. Summary of voltage stress is shown in Table 4. Modified converter with variable load and frequency are shown in Table 5 and Table 6. Variation of output voltage with the input voltage is shown in Table 7. Variation of output power with the input voltage is shown in Table 8. Table 1 Summary of steady state error. Table 2 Summary of time-domain specifications and steady state error Table 3 Summary of transient response. Table 4 Summary of voltage stress. Table 5 Modified converter with variable load. Table 6 Modified converter with variable frequency. Table 7 Variation of output voltage with the input voltage. Table 8 Variation of output power with the input voltage.

CONCLUSION

The conventional boost converter in open loop model and the closed loop model using state space method are simulated using the blocks of MATLAB-SIMULINK. The modified forward converter system using fuzzy logic and artificial neural network controller and the same system using gilberts method of tuning the state space model which is to obtain the controllability and stability are simulated using the blocks of MATLAB-SIMULINK. From the simulation results, the comparison has been done, from the two controllers which are used in this system are conventional and the modified circuit with state space model. The modified forward converter with state space model has reduced the noise in the output. The modified forward converter system using fuzzy logic, artificial neural network controller and the same system using gilberts method of tuning the state space model are compared. From the simulation results, modified forward converter system using gilberts method of tuning the state space model has reduced the noise and also tuned the output voltage. In state space model approach, the response in the modified converter with increased voltage, reduced stress, closely peak voltage and reduced the steady state error. From the comparison of results, it is observed that the modified forward converter system using the state space model is suitable for the SMPS System

### References

Lopez del Moral et al (2015). High efficiency DC-DC auto transformer forward-fly-back converter for MPPT architectures in solar plants. IEEE 9th International Conference-Compatibility and Power Electronics (CPE) Publications, date: 24-26, PP. 431-436. Ahmed et al (2015). A Feed forward Voltage Mode Controlled ZVS based Phase shifted 300W full bridge DC-DC converter for military application. IEEE Conference-Power and Advanced Control Engineering (ICPACE) Publications, date:12-14, PP.238-243. F.M.Ibanez et al (2015). Soft-switching forward DC–DC converter using a continuous current mode for electric vehicle applications. IET Power Electronics journal, Vol. 8, No.10, PP.1978-1986. M. Khalilian et al (2015). Soft-single-switched dual forward-fly-back PWM DC-DC converter with non-dissipative LC circuit. IEEE Conference-Electrical Engineering (ICEE),10-14, PP. 1562 – 1567. Fei Lu et al (2015). A Double-Sided LCLC-Compensated Capacitive Power Transfer System for Electric Vehicle. IEEE Transactions on Power Electronics, Vol.30,No.11, PP. 6011-6014. Yi-Ping Hsieh et al (2013). High conversion ratio bidirectional DC-DC converter with coupled inductor. IEEE Transactions on Industrial Electronics, Vol.61, No.1, PP. 210-222. Vijayakumar.P and RamaReddy.S (2011). Closed Loop Controlled Low Noise SMPS System Using Forward Converter. International Journal of Computer and Electrical Engineering, Vol.3, No.1, 74-78. Vijayakumar.P and RamaReddy.S (2009). Simulation Results of Double Forward Converter. International Journal the annals of dunarea dejos, University of Galati, Fascicle III, Vol.32, No.2, 51-57. Vijayakumar.P and RamaReddy.S (2013). Simulation Results of Forward Converter with Improved Efficiency for SMPS System. European Journal of Scientific Research, Vol.114, No.2, 74-78.PP.295-303. Arsalan Ansari et al (2016). A 3 kW Bidirectional DC-DC Converter for Electric Vehicles. Journal of Electrical Engineering Technology, 11(4).PP. 860-868.

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