 Hello. Myself, Sunil Kalshetti, assistant professor, department of electronics engineering, Walchen institute of technology, Solapur. Today, I am going to discuss the LEADLAC compensator, learning outcome. At the end of this session, students can analyze LEADLAC compensator. A LEADLAC compensator is a type of electrical network that generates phase lag as well as phase lead in the output signal at different frequencies when a steady state sinusoidal input is applied to it. It is also known as a LEADLAC network. In case of LEADLAC compensator, the phase lead and phase lag occurs at a different frequency region. Generally, at low frequency, phase lag characteristics is noticed in the output of the circuit while at high frequency, we have phase lead characteristics. Thus, we can say a phase LEADLAC network is a cascade combination of phase LEADLAC network. A LEADLAC compensator improves the steady state performance of the system. But at the same time, such a network causes a reduction in the overall bandwidth. A LEADLAC compensator offers increased bandwidth, thus provides a faster response. But this increases the susceptibility of the system towards the noise. Now, what is the necessity of the LEADLAC compensator? Generally, compensation in a control system is majorly done for two main reasons. Like for an absolutely unstable system, compensation is done in order to stabilize the system, while sometimes the system is stable. Still, we do not achieve the desired performance, where the desired performance on the various system performance. More simply, we can say to have the accurate transient and steady state response, a combination of LEADLAC compensator is used. Control system is added with a compensator in order to improve the specification of the control system. However, each of the compensating network introduces some drawbacks along with the improving characteristics. This is the circuit diagram of LEADLAC compensator. A combination of LEADLAC compensator is nothing but LEADLAC compensator or network. Now, let us see derive the transfer function of LEADLAC compensator. Let us obtain the transfer function of LEADLAC network. Now, the sum of current through the R1 and C1 is nothing but I of t. Therefore, EI minus E0 divided by R1 plus C1 into d by dt EI minus E0 is equal to I of t. Now, take the Laplace transform. So, the equation becomes 1 upon R1 into EI of s minus 1 upon R1 into E0 of s plus SC1 into EI of s minus SC1 E0 of s is equal to I of s equation 1. Now, the output equation I of t into R2 plus 1 upon C2 integration of I of t dt is equal to E0 of t. Now, again take the Laplace transform of this equation. So, the equation 2 becomes I of s into bracket R2 plus 1 upon SC2 is equal to E0 of s. Now, substitute the I of s from 1 in equation 2. So, we will get EI of s into 1 plus s R1 C1 into 1 plus s R2 C2 divided by s R1 C2 is equal to E0 of s into bracket 1 plus 1 plus s R1 C1 into bracket 1 plus s R2 C2 divided by s R1 C2. Now, the transfer function it becomes E0 of s divided by EI of s is equal to 1 plus s R1 C1 into 1 plus s R2 C2 divided by s square R1 R2 C1 C2 plus s into bracket R1 C1 plus R2 C2 plus R1 C2 bracket complete plus 1. Now, simplify the equation therefore, so E0 of s upon EI of s is equal to s plus 1 upon t1 into s plus 1 upon t2 divided by s plus beta upon t1 into s plus 1 upon beta t2 equation number 3 where t1 is equal to R1 C1 t2 is equal to R2 C2 beta upon t1 plus 1 upon beta t2 is equal to 1 upon R1 C1 plus 1 upon R2 C2 plus 1 upon R2 C1 and alpha beta t1 t2 is equal to R1 R2 C1 C2 and alpha beta is equal to 1. Therefore, the transfer function becomes E0 of s upon EI of s is equal to 1 plus t1 s into bracket 1 plus t2 s divided by 1 plus t1 upon beta into s into bracket 1 plus t2 beta s where beta is greater than 1. Now, pole 0 plot here 2 0s and 2 poles are available. So, the location of 0 s is equal to minus 1 upon t1 and s is equal to minus 1 upon t2 and the location of pole s is equal to minus beta upon t1 and s is equal to minus 1 upon t2 beta this is the pole 0 plot. Now, pole R plot of lead lag compensator already we know the transfer function of the lead lag compensator. So, E0 of s upon EI of s is equal to 1 plus t1 s into 1 plus t2 s divided by 1 plus t1 upon beta into s into 1 plus t2 beta s now substitute s is equal to j omega. Therefore, the transfer function in the frequency domain as follow 1 plus t1 j omega into 1 plus t2 j omega divided by 1 plus t1 upon beta into j omega into 1 plus j t2 beta omega. Now, determine the magnitude of transfer function. So, m is equal to under root 1 plus omega square t1 square into under root 1 plus omega square t2 square divided by under root 1 plus t1 square omega square divided by beta square into under root 1 plus beta square t2 square omega square. Now, the phase angle is given by phi is equal to tan inverse omega t1 plus tan inverse omega t2 minus tan inverse t1 omega upon beta minus tan inverse beta t2 omega. Now, for omega is equal to 0 m is equal to 1 phi is equal to 0 while omega is equal to infinity m is equal to 1 phi is equal to 0 this is the polar plot of lead lag compensator. Let us see effect of lead lag compensator. It is used when first response and good static accuracy is required. It increases low frequency gain which improves the steady state. The lead characteristics of the cascaded compensator provide improvement in the overall bandwidth. It increases the bandwidth of the system making system response very fast. Also, due to the use of the lag network, the steady state performance of the system gets improved. So, we can say a lead lag network provides quick response with good accuracy. Hence, we use the combination of lead lag compensator to provide required compensation to the control system. Now, give the answer of this question. The compensator required to improve both transient and the steady state response of the system is lead lag, lead lag none of these. The correct answer is lead lag compensator advantages. Due to the presence of lead lag network, the speed of the system increases because of it shifts the gain crossover frequency to higher value. Due to the presence of lead lag network, the accuracy is improved. How the speed of the system increases in lead lag network? Due to the lead lag network, the gain crossover frequency shifts to higher value. Effect of this, the speed of the system increases. These are the references. Thank you.