A Seminar Report on FPGA Based Design and Development of Distributed Arithmetic Control System.

Transcription

1 A Seminar Report on FPGA Based Design and Development of Distributed Arithmetic Control System. Submitted by: Abdul Hafeez Sajid Guide: Prof. D.G. Chougule

2 Certificate This is to certify that Mr. ABDUL HAFEEZ SAJID has satisfactorily presented a seminar on the topic FPGA BASED DESIGN AND DEVELOPMENT OF DISTRIBUTED ARTHIMETIC CONTROL SYSTEM in partial fulfillment of the requirements of M.Tech-II Sem-III (Electronics Technology) of Electronics Technology Department of Shivaji University Kolhapur, during academic year Seminar Guide Head of Department Prof. D.G. Chougule Prof. S.R. Sawant

3 Acknowledgement I wish to express my thanks to Prof. S.R. Sawant Head, Department of Electronics Technology, Shivaji University, Kolhapur for giving me an opportunity to present a seminar on FPGA Based Design and Development of Distributed Arithmetic Control System. I am thankful to Prof. D. G. Chougule for guiding and helping me in preparation of seminar. Last but not least I am thankful to Mr. M Sultan M Siddiqui, Research Scholar IIT Delhi, for guiding me to present the seminar. At last I am thankful to everyone who directly or indirectly helped me in making my efforts successful. A.H.Sajid

4 Contents 1. Abstract 2. Introduction 3. Importance of PID & its Application 4. Digital Implementation of PID 5. Advantages of Using FPGA over other Digital Techniques 6. PID Implementation using DA Algorithm 7. FPGA Architecture 8. FPGA Design Flow 9. Proposed Experimental Setup 10. Advantages of the Approach 11. Conclusion 12. References

5 Abstract

6 Introduction A control system seeks to make a physical system output track a desired reference input by setting physical system input. Designing a control system in not easy. The objective of a control system design is to make a physical system behave in a useful fashion, in particular, by causing its output to track a desired reference input even in the presence of measurement noise, model error and disturbances. e(t) þ y(t) Controller u(t) Physical System Figure: Block Diagram of a Control System. Measurement System Controller In a control system, one of the main components is the controller (control element). It is the component required to generate the appropriate control signal applied to the physical system. It measures the error or difference between the output and the desired output. The output signal of controller regulates the system performance. Many a times the function of a controller is to obtain the desirable characteristics avoiding undesired characteristics. Controller Types 1. Continuous Controller The most common controller action used in process control is one or a combination of contino i. Proportional Controller ii. Integral Controller iii. Derivative Controller 2. Discontinuous Controller i. Two-Position Controller ii. Multi-position Controller

7 3. Composite Controllers i. Proportional-Integral Controller ii. Proportional-Derivative Controller iii. Proportional-Integral-Derivative Controller PID- (Proportional- Integral- Derivative ) It is one of the most commonly used type of controller in dynamic control systems, which provides proportional, integral, and derivative compensation to an existing system. P Control Increases gain margin & stabilizes the unstable system. I Control Minimizes Steady State error. D Control Increases System Speed by increasing system Bandwidth. It does not need a precise analytical model of the system that is being controlled. Used in many different areas, such as aerospace, process control, manufacturing, robotics, automation, and transportation system. Drawback Overall System Complexity increases. Digital Implementation of PID Two approaches for implementing control systems using digital technology. 1. Based on software which implies a memory-processor interaction. Ex: PLCs, microcontrollers, microprocessors, DSPs, and general purpose computers are tools for software implementation. 2. Based on Hardware. Ex: Digital Logic & MSI Components, ASIC & FPGA. FPGA Implementation of PID 1. Conventional Approach Use of Multipliers & Adders. Requires large area on chip Consumes more power. 2. Use of DA Algorithm Is an efficient LUT design method Uses only 13% of logic devices on FPGA Power consumption is reduced by 40% Advantages of Using FPGA over other Digital Techniques 1. They ensure ease of design. 2. Lower development costs. 3. More product revenue, and the opportunity to speed products to market. 4. Real time processing Capability. 5. They are superior to software-based controllers as they are

8 6. More compact, 7. Power-efficient, while adding high speed capabilities. 8. Another advantage of FPGA-based platforms is their capability to execute concurrent operations, allowing parallel architectural design of digital controllers. Distributed Arithmetic Algorithm Distributed arithmetic is a bit level rearrangement of a multiply accumulate to hide the multiplications. Basically it is a bit serial computation operation that forms an inner product of a pair of vectors in a single direct step Arithmetic operations are not lumped but are distributed in an often unrecognizable fashion. Advantages of DA It is a powerful technique for reducing the size of a parallel hardware multiplyaccumulate that is well suited to FPGA designs. DA Algorithm uses only 13% of logic devices of FPGA to implement PID functionality compared to the design using multiplier. With DA power consumption is reduced by 40%(for PID). Concept of DA In this case we feed four parallel scaling accumulators with unique serialized data. Each multiplies that data by a possibly unique constant, and the resulting products are summed in an adder tree. Fig: Parallel multiply-accumulate based on Scaling Accumulator

9 Fig: Rearranged circuit Here, the adder tree combines the 1 bit partial products before they are accumulated by the scaling accumulator. Rearranged the order in which the 1xN partial products are summed. Instead of individually accumulating each partial product and then summing the results, first we sum all the 1xN partials & then accumulate at a particular bit time. Effectively replaces N multiplies followed by an N input add with a series of N input adds followed by a multiply. This arithmetic manipulation directly eliminates N-1 multipliers in an N product term multiply-accumulate function. For larger numbers of product terms, the savings becomes significant. If the coefficient Cn is a constant, then the adder tree becomes a Boolean logic function of the 4 serial inputs. The combined 1xN products and adder tree is reduced to a four input look up table, which further reduces hardware resource. Drawback of DA Slowness as it is a bit-serial nature. Remedy Use of bit paring technique Partitioning the input word into Half MSB & Half LSB i.e. introducing the parallelism. Consider 1. Where Ak = Fixed coefficients Xk = Input data If each Xk is a 2 s compliment binary number such that Xk is less than 1 then

10 2. Where the b kn are the bits, 0 or 1, b k0 is the sign bit, b k N-1 is the LSB. Combining equation 1 & 2 we get Equation 3 defines Lumped Arithmetic Computation Let change the order of Summation we get Equation 4 defines Distributed Arithmetic Computation. Consider the bracketed term in Equation 4 5. Since b kn can take 0 & 1 only therefore Equation 5 have 2 k possible values Rather than computing these values online, we pre-compute them & store in ROM. The I/P data can be used directly address the memory & the result of equation 5 can be dropped directly into an accumulator. After N cycles the memory contains the result y. Consider an example with K=4, A1= 0.72, A2 = -0.3,A3= 0.95, A4= The memory must contains all possible 24 combinations. As a consequence we need to use 2* 24 word ROM.

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13 PID Implementation Using DA Algorithm The simplest form of the PIDcontrol algorithm is given by u(t) = K P e + K I Int(0-t) e(τ )dτ + K D ė + offset 1 Problems with this implementation are 1. Sluggish transient response. (coz of I) 2. Detoriation of Command signal due to noise. (coz of D). 3. Spikes in Command signal (coz of D) Therefore we use a modified PIDcontrol algorithm that overcomes the above problems & is given in laplace domain as U(s) = K(bUc(s) Y(s)+(1/sTi)(Uc(s) Y(s)) (std/1+std/n)y(s)) 2 Where K, b, Ti, Td, and N are controller parameters, and U (s), Uc (s), and Y (s) denote the Laplace transforms of u, uc,& y, respectively. To implement the control algorithm using digital technology, equation (2) has to be discretized. Let T be the sampling period, and using backward differences to discretize the derivative term and forward differences for the integral term, we get u(kt ) = P (kt ) + I(kT ) + D(kT ) 3 where k denotes the k-th sampling instant P (kt ) = K(bu(kT ) y(kt )) I(kT)=I((k 1)T)+(KT/Ti)(u((k 1)T) y((k )T)) D(kT)=(Td/Td+NT)D((k 1)) (KTdN/Td+NT)(y(kT) y((k 1)T)) 4 where, y(kt) is the output of the system at the current instant, y((k 1)T) is the output of the system at the previous instant, uc (kt ) is the desired output of the system, I((k 1)T ) is the integral term at the previous instant, D((k 1)T ) is the derivative term at the previous instant, and K, b, Ti, Td, N are controller parameters,

14 The direct(multiplier & Adder/Substractor) Implementation of above algorithm us 5 Multipliers 5 Adders/Substractors 4 Delay blocks i.e. P(kT) uses 2 Multipliers & 1 Adder/Substractor I(kT) uses 1 Multipliers & 2 Adder/Substractor D(kT) uses 2 Multipliers & 2 Adder/Substractor Since Multiplier -Based Design uses many Multipliers & Adders, in order to reduce the number of Multipliers & Adders we use DA Algorithm for PID Implementation. Let us consider the controller terms given in Equation 4. Assume that u(kt), u((k-1)t), y(kt) & y((k-1)t) are M-bit numbers & [j] represents the jth bit of number then We have m 1 P(kT) = Ʃ (Kb u(kt)[ j] K y(kt)[ j]) 2j 5 j=0 m 1 I(kT) = Ʃ (I((k 1)T)[ j] + (KT/Ti)(u((k 1)T)[ j] y((k 1)T)[ j])) 2j 6 j=0 m 1 D(kT ) = Ʃ ((Td/Td+NT)D((k 1)T)[ j] (KTd N/Td + NT)((y(kT )[ j] y ((k 1) T ) j=0 [ j]) 2 j)) 7 The results of (Kb u(kt)[ j] K y(kt)[ j]), I((k 1)T)[ j] + (KT/Ti)(u((k 1)T)[ j] y((k 1)T)[ j]))((td/td+nt) D((k 1)T)[ j] (KTdN/Td + NT)((y(kT )[ j] y((k 1)T)[ j]) 2 j)) can be pre-computed & the result can be stored in 3 LUT's namely LUTp, LUTi, & LUTd. Using the 3 LUTs and the corresponding shift-add accumulators (ACCs), the P (kt), I(kT), and D(kT) terms can be obtained in m clock cycles. Main advantage of the DA expression given by (5), (6) and (7) lies in its capability to compute the PID function utilizing the LUT-rich FPGA. Based on the above Equations the DA Implementation of PID Controller is shown in Fig

15 It consists of 4 delay blocks, 3 LUT's, 3 ACC's & 2 Adders. i.e. 3 LUTS's & 3 ACC's for P(kT),I(kT) & D(kT). ACC consists of shift register & adder 2 Adders to produce sum of P(kT),I(kT) & D(kT). Speed of this PID is M+1 clock cycles i.e. M clock cycles to generate the result & 1 clock cycle to update the I((k 1)T) and D((k 1)T) terms. FPGA Architecture The typical FPGA consists of the following components: 1. Programmable Logic blocks 2. Interconnection Resources 3. Input output blocks The general schematic of an FPGA is as shown in the figure :

16 Programmable Logic Block The programmable logic block in a typical FPGA consists of Configurable Logic Blocks (CLB). The CLB can be realized in many ways; one of them being the Look Up Table (LUT) based CLB. The LUT is a one bit wide memory location. The memory address lines are the inputs to the LUT and the one bit output is the LUT output. Thus the LUT with K-inputs acts as a 2k by 1 bit memory and the user can directly implement any k input function by programming the functions truth table into the LUT

17 Fig: Xilinx FPGA CLB Schematic Interconnect Resources The interconnect resources in an typical FPGA can be classified as : 1. General Purpose Interconnects 2. Direct Interconnects 3. Long Lines Input Output Blocks (IOB) The IOB provides the interface between the FPGA and the real world signals. The IOB consists broadly of I/O pads. DA-based PID controller is to be implemented using the Xilinx Inc. FPGA technology. ie. SPARTAN IIE Xc2s200e-FT256 The FPGA design flow is as follows: 1. Controller is implemented using pico blaze a soft processor developed by xilinx. 2. Simulation at RTL level to verify the correctness of design. 3. Place & route is done automatically to generate FPGA implementation file.

18 4. Finally the generated implementation file was downloaded to the FPGA development board for testing. Proposed Experimental Setup The FPGA-based temperature control system that is shown in Fig. 1) A tube with a fan, a light bulb, and a thermistor; 2) An I/O panel 3) An ADC chip (Maxim MAX bit ADC) 4) FPGA development board consisting a Xilinx Spartan-2E FPGA Conclusion The proposed PID controller reduces the cost of the FPGA design. Due to the flexibility of the LUT in the FPGA, this FPGA-based PID controller can be easily extended to incorporate other algorithms, This design approach would specifically be suitable for the next generation of FPGA chips, in which ADC and D/A converter are built inside the chip. References K. J. Astrom and B. Wittenmark, Computer Controlled Systems. Englewood Cliffs, NJ: Prentice-Hall, L. Samet, N. Masmoudi, M. W. Kharrat, and L. Kamoun, A digital PID controller for real-time and multi-loop control: A comparative study, in Proceedings of IEEE International Conference Electron., Circuits and Systems, Sep. 1998, vol. 1, pp

19 B. Wittenmark, K. J. Astrom, and K-E., Arzen, Computer Control: An Overview, Technical Report, Department of Automatic Control, Lund Institute of Technology, Sweden ( kursdr/ifac.pdf), April R. Chen, L. Chen, and L. Chen, System design consideration for digital wheelchair controller, IEEE Trans.. Ind. Electronics, vol. 47, no. 4, pp , Aug Altera Flex10 K Embedded Programmable Logic Family Data Sheet, 2003, San Jose, CA: Altera Corp. [Online]. Available: R. Ruelland, G. Gateau, T. A. Meynard, and J.-C. Hapiot, Design of FPGA-based emulator for series multi-cell converters using co-simulation tools, IEEE Trans. Power Electronics., vol. 18, no. 1, pp ,Jan K. Sridharan and T. K. Priya, The design of a hardware accelerator for real-time complete visibility graph construction and efficient FPGA implementation, IEEE Trans. Ind. Electronics., vol. 52, no. 4,pp , Aug M. Gabrick, R. Nicholson, F. Winters, B. Young, and J. Patton, FPGA considerations for automotive applications, in Proc. SAE Conf., 2006, CD-ROM. Mikulá s Huba and Miroslav Simunek Modular Approach to teaching PID Controller, IEEE Trans. Ind. Electronics, vol. 54, no. 6,dec Eric Monmasson, and Marcian N. Cirstea FPGA Design Methodology for Industrial Control Systems A Review IEEE Trans. Ind. Electronics, vol. 54, no. 4, Aug V. Sornam Viswanathan Embedded Control Using FPGA Seminar Report Interdisciplinary Programme in Systems and Control Engineering Indian Institute of Technology, Bombay. Y.F. Chan M. Moallem W. Wang Efficient Implementation of PID Control Algorithm using FPGA Technology 43rd IEEE Conference on Decision and Control December 14-17, 2004 Atlantis, Paradise Island, Bahamas Yuen Fong Chan, M. Moallem, and Wei Wang, Design and Implementation of Modular FPGA-Based PID Controllers IEEE Trans. Ind. Electronics, vol. 54, no. 4, Aug