FPGA Implementation of Linear Model Predictive Controller for Closed Loop

Control of Intravenous Anesthesia

Guide:-Prof. D. N. Sonawane

By:-Prashant Basargi(121117003)

Objectives• Understanding Linear MPC and QP problem• Active-set method• Hardware/Software Co-Simulation• Testing of developed MPC architecture for closed loop

control of intravenous anesthesia • Simulation of various clinical trials

Model Predictive Control:

Block Diagram MPC strategy

Types of Model Predictive Control:

Tuning parameters of MPC:

1. Sample time2. Prediction horizon3. Control horizon

Methods to solve QP problems :

1.Active set method

2.Interior point method

3.Gradient Projection method

Why Active Set ?

• Best suitable for less numbers of variables• Gives more exact solutions and sensitivity

information for less number of variables

• Active set methods are more stable than interior-point methods for less numbers of variables

Hildreth Algorithm:

1. Find initial values of X– Find H-1 matrix– Cholesky decomposition [L and LT] – Inverting triangular matrix [L-1 and (LT)-1] – Multiplication of L-1 and (LT)-1 – Multiplication of H-1, C and -1

2. Find optimum values of λ

P=M x H-1 x MT

– Multiplication of M and H-1 – Multiplication of above calculated matrix and MT

Continued…3. d = (M x H-1 x C) + K

– multiplication of M, H-1 and C – Addition of above calculated matrix and K matrix

4. Using lower triangular matrix of P calculate the values of λ 11, λ 2

1, λ 31.

5. Using matrix P and above calculated values of λ find values of λ 12, λ 2

2, λ 32.

6. Using this optimum value of λ calculate optimum value of X* by,

X* = X - H-1 x MT x λ* – Multiplication of H-1, MT and λ*– Subtract above calculated value from initial value of X.

Cholesky decompositionA = L * L

Algorithm:1. Determine l11 and L21

2. Compute L22 from

Synthesis report:Device Utilization Summary (estimated values) [-]

Logic Utilization Used Available UtilizationNumber of Slice Registers 2023 54576 3%Number of Slice LUTs 7493 27288 27%Number of fully used LUT-FF pairs 1449 8067 17%

Number of bonded IOBs 833 296 281%Number of BUFG/BUFGCTRLs 1 16 6%Number of DSP48A1s 8 58 13%

MATLABExecution time=0.001152sec=1152000 nsec

FPGAClock cycle required=24 Execution time=120 nsec

Hildreth Algorithm: synthesis report

MATLABExecution time=0.826691 sec = 826691 microsec

FPGAClock cycle required=224 Execution time=1.12 microsec

Device Utilization Summary (estimated values) [-]Logic Utilization Used Available UtilizationNumber of Slice Registers 5278 54576 9%Number of Slice LUTs 13425 27288 49%

Number of fully used LUT-FF pairs 4127 14576 28%

Number of bonded IOBs 1217 296 411%Number of BUFG/BUFGCTRLs 1 16 6%Number of DSP48A1s 8 58 13%

Fix to float synthesis report:

Results:Input number Expected output Proposed IP core output

5.34 32’h40AAE148 32’h40AAE148

-11.57 32’hC1391EB8 32’hC1391EB8

0.023 32’h3CBC6A7F 32’h3CBC6A40

Device Utilization Summary (estimated values)Logic Utilization Used Available UtilizationNumber of Slice Registers 11 54576 0%Number of Slice LUTs 480 27288 1%Number of fully used LUT-FF pairs 11 480 2%

Number of bonded IOBs 65 296 21%Number of BUFG/BUFGCTRLs 1 16 6%

Addition/Subtraction Synthesis report:

Results:Input number1 Input number2 Expected output

Addition/subtractionProposed IP core output

Addition/subtraction32’h41280000 32’h40AAE148 32’h417D70A4/

32’h40A51EB832’h417D70A0/32’h40A51EB8

32’h405AE148 32’hC1391EB8 32’hC1026666/32’h416FD70A

32’hC1026666/32’h416FD70A

 

Device Utilization Summary (estimated values) [-]

Logic Utilization Used Available Utilization

Number of Slice Registers 31 54576 0%

Number of Slice LUTs 573 27288 2%

Number of fully used LUT-FF pairs 31 573 5%

Number of bonded IOBs 97 296 32%

Number of BUFG/BUFGCTRLs 1 16 6%

Multiplication Synthesis report:

Results: 

Device Utilization Summary (estimated values)

Logic Utilization Used Available Utilization

Number of Slice LUTs 54 27288 0%

Number of fully used LUT-FF pairs 0 54 0%

Number of bonded IOBs 97 296 32%

Number of BUFG/BUFGCTRLs 1 16 6%

Number of DSP48A1s 4 58 6%

Input number1 Input number2 Expected outputMultiplication

Proposed IP core outputMultiplication

32’h41280000 32’h40AAE148 32’h426047AE 32’h

32’h405AE148 32’hC1391EB8 32’hCC21E4711 32’h

Division Synthesis report:

Results: 

Device Utilization Summary (estimated values)Logic Utilization Used Available UtilizationNumber of Slice LUTs 1757 27288 6%

Number of fully used LUT-FF pairs 0 1757 0%

Number of bonded IOBs 97 296 32%

Number of BUFG/BUFGCTRLs 1 16 6%

Input number1

Input number2 Expected outputDivision

Proposed IP core outputDivision

32’h41280000 32’h40AAE148 32’h3FFBAF76 32’h

32’h405AE148 32’hC1391EB8 32’h3E9757D7 32’h

Square root synthesis report:

Results:Input number Expected output

Square rootProposed IP core output

Square root5.34 32’h4013E4DE 32’h4013E4DE

11.57 32’h4059B1B0 32’h4059B1B0

0.023 32’h3E1B4C1B 32’h3E1B4C1B

 

Device Utilization Summary (estimated values) [-]Logic Utilization Used Available UtilizationNumber of Slice LUTs 900 27288 3%

Number of fully used LUT-FF pairs 0 900 0%

Number of bonded IOBs 64 296 21%Number of BUFG/BUFGCTRLs 1 16 6%

Objective completed:

• Different IP cores :o IEEE 754 Floating Point Number

Converter and Arithmetic unitso Matrix algebrao Cholesky Decompositiono Active set method

Objective to be completed:

• Hardware/Software Co-Simulation• Testing of developed MPC architecture for

closed loop control of intravenous anesthesia.• Simulation of various clinical trials

Literature Survey

• E. Furutani and Y. Sawaguchi, “A hypnosis control system using a model predictive controller with online identification of individual parameters”, Proceedings of the 2005 IEEE Conference on Control Applications Toronto, Canada, August 28-31, 2005,154-159.

• N. Cardoso and J.M. Lemos, “Model Predictive Control of depth of Anesthesia: Guidelines for controller configuration”, 30th annual international IEEE EMBS conference vancouver, british columbia, canada, August 20-24, 2008.

• D. Ingole, D. N. Sonawane, V. Naik, D.Ginoya, V. Patki, “Implementation of Model Predictive Control for Closed Loop Control of Anesthesia”, proceeding of the third International Conference on control, communication and power engineering (CCPE-2012),Bangalore, India: Springer-Verlag,2012, pp.415-421.

Fix to float conversion:

Addition/subtraction :

Multiplication:

Division: