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RS dc-dc converter 2004

  2. 2.  Innovated by C. Sreekumar and Vivek Agarwal, Senior Member, IEEE  IEEE transactions on industrial electronics, Volume 55, No. 6, June 2006  Presented by:  Utsav Yagnik  M.E. Electrical(Roll No. 2004)  Shantilal Shah Engineering College, Bhavnagar ABOUT THE PAPER 2
  3. 3. 3 Sr. Slide title From To 1 Abstract 4 6 2 Introduction 7 7 3 Earlier Approaches 8 11 4 Typical DC-DC Boost Converter 12 12 5 Hybrid Modelling & Automation Representation 13 21 6 Guard Selection Problem 22 22 7 CCM Operation 23 28 8 DCM Operation 29 31 9 Guard conditions 32 32 10 Simulation Parameters 33 33 11 Simulation Results 34 34 12 Operation at CCM-DCM boundary 35 36 13 Operation Under Input Voltage Disturbances 37 37 14 Impact of Higher Trap Frequency 38 40 15 Experimental Verification 41 41 16 Conclusion 42 42 17 Salient Features 43 45 I N D E X
  4. 4. A state trajectory approximation based switching control to regulate the output voltage of a representative second order dc-dc converter. Main objective is to trap the system in a stable limit cycle, but without violating the limits of voltage regulation. The difference between this method and earlier methods is the applicability to the CCM and DCM modes of opration. ABSTRACT 4
  5. 5. Which makes this algorithm suitable over wide range of load and various disturbances. The control problem is simplified to guard selection problem by introducing the Hybrid automation representation. In this Hybrid automation representation, the guard conditions are derived which are governing the transition from one discrete state to another. This algorithm is implemented by State Flow Chart method in MATLAB. ABSTRACT 5
  6. 6. The hybrid control law is also validated by using a laboratory prototype. So, all in all this whole algorithm and hybrid model is used to find a single model which will be suitable for both CCM and DCM modes of operations. ABSTRACT 6
  7. 7. DC-DC converters are: 1. Highly non-linear 2. Discontinuous in time 3. Variable in structure(i.e. they work under various topologies based on the mode of operation) 4. CCM and DCM Complete range of converter will include CCM and DCM So, we need a common representation that will cover entire operating range. INTRODUCTION 7
  8. 8. Using transfer function: States of system are averaged around a normal point and linearized via s-domain. Same thing can be achieved by Langrangian approach in time domain. Now a days we can also get Numerical state space value model for control design. But all above will describe dynamics around operating point but will fall short when disturbances occur EARLIER APPROACHES 1 8
  9. 9. We can also design State space model But it will also require different models for CCM and DCM. Sometimes DCM is overlooked if persisted for shorter duration. EARLIER APPROACHES 2 9
  10. 10. One can also go for PWM(Pulse Width Modulation) which has which has two types of control: 1. Voltage mode control 2. Current mode control But both of above will have inherent instability and sub harmonic oscillations when operated under constant frequency PWM. EARLIER APPROACHES 3 10
  11. 11. We can also do Linear system design techniques in frequency domain. But it also has constraints of right hand plane zero in average model. And since the location of zero is inversely proportional to inductor current, as we increase the load current, the zero will go towards low frequency. This will introduce phase lag and result in less availability of band width. EARLIER APPROACHES 4 11
  13. 13. 𝑥 = 𝑅 𝑛 is a continuous state space. 𝑄 = 𝑞1, 𝑞2, … 𝑞 𝑛 are finite set of discrete states. The continuous state space specifies the possible values of the continuous states for all q’s and q ε Q shows ON/OFF configurations. HYBRID MODELLING AND AUTOMATION REPRESENTATION 13
  14. 14. The common state space equation is 𝑥 𝑡 = 𝐴𝑞𝑥 𝑡 + 𝐵𝑞 = 𝑓𝑞 𝑥 𝑡 Where 𝑥 ∈ 𝑋, 𝐴𝑞 ∈ 𝑅 𝑛 × 𝑛 𝑎𝑛𝑑 𝐵𝑞 ∈ 𝑅 𝑛 ×1 If k are switching elements then 2 𝑘 are possible discrete states. HYBRID MODELLING AND AUTOMATION REPRESENTATION 14
  15. 15. State SW1 SW2 𝑞1 ON OFF 𝑞2 OFF ON 𝑞3 OFF OFF 𝑞4 ON ON HYBRID MODELLING AND AUTOMATION REPRESENTATION where, SW1 = main controllable switch SW2 = power diode 15
  16. 16. Here 𝑞4 is not possible because it will bypass the load. ∴ 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑄 = 𝑞1, 𝑞2, 𝑞3 ∴ total possible events E = 𝑞1, 𝑞2 , 𝑞2, 𝑞1 , 𝑞2, 𝑞3 , 𝑞3, 𝑞1 First two events corresponds to the CCM operation and 1st, 3rd & 4th events corresponds to DCM operation. HYBRID MODELLING AND AUTOMATION REPRESENTATION 16
  17. 17. States of the system are taken as (𝑖 𝐿, 𝑣 𝑜). Where, 𝑖 𝐿 = Instantaneous Inductor Current & 𝑣 𝑜 = Instantaneous Output Voltage Let, 𝑉 𝑚 = Input voltage L = Input inductor C = Output capacitor R = Load resistance HYBRID MODELLING AND AUTOMATION REPRESENTATION 17
  18. 18. Thus, the system can be represented in terms of three state equations corresponding to the 𝑞 𝑖(1,2,3) as below… HYBRID MODELLING AND AUTOMATION REPRESENTATION 18
  19. 19. Under closed loop conditions, control operation can be considered as an interacting combination of two hybrid automations. In which, the discrete evaluation depends upon continuous signal 𝑥(𝑡) and the continuous evaluation depends upon discrete symbol 𝜎 = 𝜎1, 𝜎2, 𝜎3 HYBRID MODELLING AND AUTOMATION REPRESENTATION 19
  20. 20. Here, the control problem is to find guard conditions 𝐺 𝑖𝑗 which cause transition from 𝑖 𝑡ℎ discrete state to 𝑗 𝑡ℎ discrete state while satisfying the system requirements. In this paper, approach is to determine appropriate switching guards for trapping the system in to a limit cycle satisfying the Voltage regulation constraints. HYBRID MODELLING AND AUTOMATION REPRESENTATION 20
  22. 22.  For CCM, we need to determine two guards. i.e. 𝐺12 and 𝐺21.  For DCM, we need to determine three guard. i.e. 𝐺12, 𝐺23 𝑎𝑛𝑑𝐺31.  The generation of control pulses depends upon similar conditions based on the respective guards except that in the CCM mode, the third mode is not present, and transitions from mode 2 to mode 3 and mode 3 to mode 1 are not defined.  Transition from one mode to other mode takes place when the sensed state variables exceed the relevant guard conditions. GUARD SELECTION PROBLEM 22
  23. 23. CCM OPERATION 23
  24. 24. At dT, system dynamics changes from mode 1 and mode 2. At T, system switches back to mode 1. During 0 ≤ 𝑡 ≤ 𝑑𝑇 𝑑𝑖 𝐿 𝑑𝑡 = 𝑉𝑖𝑛 𝐿 ∴ 2∆𝑖 𝐿 = 𝑉𝑖𝑛 𝐿 𝑑𝑇 … (1) CCM OPERATION 24
  25. 25. Also, 𝑑𝑣 𝑜 𝑑𝑡 = −𝑉𝑜 𝑅𝐶 ∴ −2∆𝑣 𝑜 = −𝑉𝑜 𝑅𝐶 dT … 2 From (1) & (2) ∆𝑖 𝐿 = 𝑅𝐶𝑉 𝑖𝑛 𝐿𝑉 𝑜 ∆𝑣 𝑜 … (3) CCM OPERATION 25
  26. 26. The ripples in the output voltage and inductor current are related by equation 3. In CCM, for the given voltage swing, the current swing along with the average inductor current is used to define the guard conditions, which governs the transition between two modes of operation. CCM OPERATION 26
  27. 27. The average inductor current can be determined by equating the converter output power with converter input power as below 𝐼 𝐿 = 𝑉 𝑜 2 𝑅𝑉 𝑖𝑛 … (4) From equations 3 and 4 the guard conditions are: 𝐺12 → 𝑖 𝐿 ≥ 𝐼 𝐿 + ∆𝑖 𝐿 𝐺21 → 𝑖 𝐿 ≤ 𝐼 𝐿 − ∆𝑖 𝐿 CCM OPERATION 27
  28. 28. These guards cause the system to settle in some limit cycle, depending upon the load conditions of the system. The load current an the output voltage have to be sensed to determine the guards. As the load decreases, the average inductor current reduces and becomes exactly half of the current ripple at the CCM-DCM boundary. Thereafter, voltage regulation is lost and the algorithm is modified for the DCM operation. CCM OPERATION 28
  29. 29. DCM OPERATION 29
  30. 30. The output voltage 𝑉𝑜 = 𝑉𝑖𝑛 𝑑1 + 𝑑2 𝑑2 The inductor current 𝐼 𝐿 = 𝑉 𝑜 𝑑1+𝑑2 𝑅𝑑2 Or 𝐼 𝐿 = 𝐼 𝑝 𝑑1+𝑑2 2 Where, 𝐼 𝑝 = 2𝑉 𝑜 𝑉 𝑜 −𝑉 𝑖𝑛 𝑅𝑓𝐿 … (5) DCM OPERATION 30
  31. 31. To define the guard condition 𝐺12, based on 𝐼 𝑃 should satisfy the equation 5. Which means that 𝐺12 depends on frequency. So the condition for the trap frequency can be obtained as below… 𝑓 𝑇 > 𝑉𝑜 − 𝑉𝑖𝑛 2∆𝑣 𝑜 𝑅𝐶 … (6) DCM OPERATION 31
  32. 32. 𝐺12 → depends on equation 5 and equation 5 depends on equation 6. 𝐺23 → natural guard, i.e. transition from mode 2 to mode 3 is autonomous due to 𝑖 𝐿 = 0. 𝐺31 → the reference voltage 𝑣 𝑜 = 𝑉𝑜 can be taken as guard condition for controlling ∆𝑣 𝑜 swings. GUARD CONDITIONS 32
  33. 33. The proposed algorithm is tested in MATLAB with following parameters: 1. 𝑉𝑖𝑛 = 15 𝑉 2. 𝑉𝑜𝑢𝑡 = 30 𝑉 3. 𝑅 = 20 Ω 4. 𝐿 = 350 𝜇𝐻 5. 𝐶 = 10 𝜇𝐹 6. ∆𝑣 𝑜 = 0.5 𝑉 SIMULATION PARAMETERS 33
  36. 36. At 6ms, when the load is abruptly changed from 45 Ω to 95 Ω, the voltage jumps to 31.2 V but soon settles down the desired value of 30 V as shown in the figure earlier. So, the transient response during transition from CCM to DCM is found satisfactory and the system does not become UNSTABLE. OPERATION AT CCM-DCM BOUNDARY 36
  37. 37. According to slide no. 35, A step rise of 5V in the input is given at 18 ms. A Sinusoidal disturbance of peak 2 V at frequency of 4000 rad/s is given. But the system can withstand these as it doesn’t become unstable. OPERATION UNDER INPUT VOLTAGE DISTURBANCES 37
  38. 38. For earlier waveforms, the trap frequency was 20 kHz. Trap frequency has minimum value of 3.9 kHz for 400 Ω and is as high as 16.6 kHz for load of 95 Ω. And now trap frequency of 30kHz is applied for the load of 440 Ω and it is observed that system remains stable. IMPACT OF HIGHER TRAP FREQUENCY(𝑓 𝑇) 38
  40. 40. A higher trap frequency is desirable as far as the speed of response, voltage ripple, current ripple and regulations are considered. But such frequency should be considered only and only if the other parameters such as power loss, driver circuit limitations, device speed etc. permit. IMPACT OF HIGHER TRAP FREQUENCY(𝑓 𝑇) 40
  41. 41. Experimental verification of control circuit in real time is done by using analogue and digital ICs and other discrete components and similar waveforms are observed. For SW1 MOSFET IRF450 and for SW2 CSD 10030 ultrafast diode are used. EXPERIMENTAL VERIFICATION 41
  42. 42. A new technique for hybrid control of dc-dc boost converter is proposed in which the control problem is simplified in to guard selection problem in a hybrid automation system to obtain required voltage regulation. Simulation is done in MATLAB/SIMULINK using the state flow chart feature. CONCLUSION 42
  43. 43. Minimal computations in algorithm making it good choice for real time control. Complete cycle of operation i.e. CCM and DCM are covered. The approach is generic and can be implemented for other similar second order converters. The proposed control has variable switching frequency with the maximum allowable output voltage ripple in the CCM operation. SALIENT FEATURES 43
  44. 44. The operation in the DCM is very smooth even under disturbances, but since the guard conditions depend upon the load value, accurate load sensor is required. PWM control is not applied. Here, the output filter capacitor value is taken as 10 𝜇𝐹. A higher value of filter capacitor will improve transient response but finer tuning of trap frequency might be required in DCM operation. SALIENT FEATURES 44
  45. 45. The load is varied by toggle switch in this experiment so the change in the switch will change in its dynamics and will effect operation. The parasitic elements are not considered to reduce the computational complexity. Nevertheless, it is proved through practical experiments that the given scheme gives good regulation characteristics over a wide range of load and line disturbances. SALIENT FEATURES 45
  46. 46. THANK YOU 46