ME4718 Sample Assignment Kaghazchi, 8193193 v2 1 NOTE: Experimental data not available for this system Plant: Blending system 1.Introduction The process of blending is the homogenous distribution of differing materials and is usually a relatively gentle process. This involves, either solid-solid mixing or the mixing of bulk solids with small quantities of liquid. Chemical blending is used in a wide variety of industries and has many applications. Blending can improve product quality, coat particles evenly, diffuse liquids or fuse particles together. Chemical blending is fully customizable – it can produce the chemical which has the exact characteristics required. Chemical blending is widely used in many industries such as: paints, soaps and cosmetics, fertilizers and powdered detergents. ME4718 Sample Assignment Kaghazchi, 8193193 v2 2 Notation: 1. w 1 , w 2 and w are mass flow rates 2. x 1 , x 2 and x are mass fractions of component A Assumptions: 1. x 2and w1 constant 2. x 1 vary 3. Perfect mixing in the tank ME4718 Sample Assignment Kaghazchi, 8193193 v2 3 2. Block diagram, and transfer functions for measurement, plant, etc. using step input 2.1 System block diagram 2.2 Experimental Transfer functions ME4718 Sample Assignment Kaghazchi, 8193193 v2 4 3. Mathematical Model Mass Balance As density and Volume are constant. w=w1+w2 Component balance Writing for steady state of above equation: Subtract above two equations and using deviation variables: Taking Laplace transform (replace d/dt with s) Where wxxwxw dt dx V 2211 xwxwxw 22110 ' 22 ' 1 ' 1 ' xwxwxw dt xd V )()()()( ''22 ' 11 ' swXsWxsXwsVsX )( 1 )( 1 )( '2 2' 1 1' sW s K sX s K sX w w K 11 w V w x K 22 1 )( )( )( 1 1' 1 ' s K sG sX sX 1 )( )( )( 2 2' 2 ' s K sG sW sX ME4718 Sample Assignment Kaghazchi, 8193193 v2 5 The nominal steady state conditions are w 1 =10kg/sec, w 2 =0.033kg/sec, x 1 =0.050, and x 2 =1. The liquid volume and density are constant V=2m 3 and ρ=900 kg/m 3 For the control valve assume that the controller output 4-20mA corresponds to 0-4kg/min of flow rate. Hence Kv=4/16=0.25kg/min/mA. Assume a time constant of 5 sec Assume a small time delay for plant, and also the dynamics of Analyser/transmitter is negligible. 4.179 033.10 )2)(900( w V 997.0 033.10 101 1 w w K 1.0 033.10 12 2 w x K 14.179 997.0 1 )( 1 ss K sGd 14.179 1.0 1 )( 2 ss K sGp 15 25.0 1 )( ss K sG v v v ME4718 Sample Assignment Kaghazchi, 8193193 v2 6 4. Controller design, tuning & implementation 4.1 Design of single loop PID controller Initial scope settings: ME4718 Sample Assignment Kaghazchi, 8193193 v2 7 4.2 Controller Tuning Z-N reaction curve method used here for controller tuning. Using Transfer function for the plant with Time delay=5sec, Time constant=180 sec, and Gain=0.1 sec/kg Controller P Controller P 360 - - PI 321 16.67 - PID 428 10 2.5 Note that Z-N continuous cycling, and auto tuning to be added here. I D ME4718 Sample Assignment Kaghazchi, 8193193 v2 8 4.3Controller performance P-control, ZN-Reaction Curve. SP-Change 0.001 Note other tuning methods to be added to graph. P-control, ZN-Reaction Curve. Load-Change 0.001 Note other tuning methods to be added to graph. ME4718 Sample Assignment Kaghazchi, 8193193 v2 9 PI-control, ZN-Reaction Curve. SP-Change 0.001 Note other tuning methods to be added to graph. PI-control, ZN-Reaction Curve. Load-Change 0.001 Note other tuning methods to be added to graph. ME4718 Sample Assignment Kaghazchi, 8193193 v2 10 PID-control, ZN-Reaction Curve. SP-change 0.001 Note other tuning methods to be added to graph. PID-control, ZN-Reaction Curve. Load-change 0.001 Note other tuning methods to be added to graph. ME4718 Sample Assignment Kaghazchi, 8193193 v2 11 Controller Set-point Response to SP, ISE Response to Disturbance ISE P-ZN-RC 0.001 PI-ZN-RC 0.001 3.038x E-5 PID-ZN-RC 0.001 1.81x E-5 PI-ZN-CC 0.001 PID-ZN-CC 0.001 PI- Auto Tuning 0.001 PID- Auto Tuning 0.001 ME4718 Sample Assignment Kaghazchi, 8193193 v2 12 5.Stability of Control loop 6.PID sampling time, determination and Influence 7.Conclusions
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