 Welcome myself, Mr. Giridhar Jain, Assistant Professor in Electronics and Telecommunication Engineering, Walchin Institute of Technology, Saulapur. Today, I am going to explain Proportional Controller. Learning outcomes of the session are, at the end of the session, students will be able to draw circuit diagram and derive expression for output voltage for proportional controller. Second outcome is, students will be able to design proportional controller. Contents of the session are, circuit of proportional controller, derivation of output voltage and design of proportional controller. So, figure shows the circuit diagram using operational amplifiers for proportional controller. So, this first operational amplifier circuit is a circuit of difference amplifier. And the input R-P-P-V, this is process variable, that is, voltage proportional to the process variable. Now, this voltage proportional to the process variable is obtained by using transducer bridge and instrumentation amplifier. So, output of instrumentation amplifier is a voltage proportional to the physical parameter to be measured. So, this is V-P-V. And this V-S-P is a set point voltage or the set point of the process is set by varying this potentiometer, one end of this potentiometer connected to 5 volt and one connected to the ground as shown in figure. Second, so this first operational amplifier will act as a error amplifier. That is, a difference between V-S-P and V-P-V means output voltage is equal to error voltage V-S-P minus V-P-V for this first stage. And second stage is inverting summing amplifier which will act as a proportional controller. And last stage is inverting amplifier with a gain of minus 1. Now, derivation for output voltage. Now, first operational amplifier circuit is a difference amplifier. Therefore, if RF is equal to R-3 and R-1 is equal to R-2, then V-O-1 is equal to V-S-P minus V-P-V into RF by R-1. Now, let RF is equal to R-1 and V-O-1 is V-Error. That is V-S-P minus V-P-V. Hence, we get V-O-2 equal to minus in the bracket V-Error into RF by R-I plus V-O-S into RF upon R-O-S bracket close. And third op-em stage is inverting amplifier with gain of minus 1. Therefore, V-O-T is inverted. Therefore, this minus sign will become plus. So, V-O-3 equal to V-Error into RF by R-I plus V-O-S into RF by R-O-S. Now, let RF equal to R-O-S. Hence, V-O-3 equal to V-Error into RF upon R-I plus V-O-S. So, this is equation of straight line Y is equal to MX plus C, where slope of the straight line M is given by RF by R-I and C is the intercept on Y axis that is V-O-S. So, in this straight line, Y is output voltage of the proportional controller and X is the V-Error that is the error voltage. Now, transfer curve for this equation V-O-3 is equal to V-Error RF by R-I plus V-O-S which is equation of straight line can be drawn like this. So, this figure shows the controller transfer curve means output is taken on Y axis and on the X axis the error is taken. So, error is nothing but V-SP minus V-PV. This P-V stands for proportional band. So, here you can observe during the proportional band this is Y is equal to MX plus C straight line so linear variation. Now, if error maximum error is there then or when the output reaches 100 percent of that then it will remain constant and on this side it will be 0. So, this is transfer curve or transfer characteristic of this proportional controller. Now pause this video and think on the following question. How does this controller differ from on-off controller? So, basically on-off controller as the name indicates on-off controller so controller output is either on or off when controller output is on it is 100 percent and when it is off 0 percent power is delivered to the load and for the proportional controller output here is linearly with V error that is error voltage in proportional band. Now, design of proportional controller. So, let us take this example design proportional controller to meet following specifications. Proposional band is equal to 67 percent. Error maximum plus minus 3 volt. Full scale output equal to 12 volt. Zero error reaches 25 percent controller output. So, this is the design task given for the design. Solution. Slope of transfer curve is given by m is equal to phi f s that is full scale voltage output divided by percentage proportional band multiplied by phi error max. So, in this design phi full scale so if we read the numerical carefully then full scale output is given as a 12 volt means phi f s is 12 volt. Then proportional band is given as a 67 percent and the phi error. So, phi error maximum error maximum is given as a plus minus 3 volt therefore maximum error is difference between plus and minus 3 that is 6 volt. Now, m equal to substituting the values m is equal to 12 in the bracket 0.67. Well divided by 0.67 into 6 that is equal to 2.98. So, this is value of m that is slope of the state line. Now, m is equal to Rf upon Ri therefore, Rf is equal to 2.98 Ri. Now, select Ri is equal to 1 kilo therefore, Rf is approximately 3 kilo and Ros is equal to 3 kilo 0 error controller output is 25 percent of phi f s that is 0.25 into phi f s is 12. So, 12 into 0.25 is 3 volt. Therefore, phi os is equal to 3 volt which is intercept on the y axis and equation for the transfer curve becomes phi o is equal to 2.98 into phi error plus 3. Now, when phi o is equal to 0 then phi error equal to 0 minus 3 divided by 2.98 that is 1 minus 1.005 volt and now when phi o is equal to 100 percent that is 12 volt then phi error is 12 minus 3 divided by 2.98 that is 3.02. So, these are the boundaries of the error 3.02 on maximum side and minus 1.005 volt on the minimum side. Now, equivalent transfer curve of the design is given below. So, this is the equivalent transfer curve of the design. So, this is output and this is the error. So, these are the boundaries of the error this is PBU PBR. Now, circuit diagram of the complete design and the component values are as given below. So, this is circuit diagram of the design. So, for the first operational amplifier R1 is equal to R2 is equal to R3 is equal to Rf is equal to 1 kilo ohm and for remaining Rf is equal to ROS is equal to 3 kilo ohm, Ri is equal to 1k R compensation which is parallel combination of Ri and Rf that is 1k and 3k 750 ohms, Rp is equal to 10 kilo ohm pot select power supply as a plus minus V is equal to 12 volt plus V is equal to 12 volt and minus V is equal to minus 12 volt. So, these are the references. Thank you for watching this video.