 Hello, myself Sunil Kalshati, assistant professor, department of Electronics Engineering, Walchand Institute of Technology, Solaapur. Today, I am going to discuss the LEAD compensator, LAC compensator, learning outcome. At the end of this session, students can analyze LAC compensator, LAC compensator. It is a circuit which is designed to generate a steady state sinusoidal signal having phase lag to the applied sinusoidal input signal. This can also be stated in a way that it is a circuit that is when provided with a sinusoidal input produces a sinusoidal output signal whose phase lags the applied input. The phase lag occurs in low frequency region. We know that compensators are used in the control system in order to have the desired output. It is achieved when the system properly controls the ongoing process inside it. When certain parameters of the system are changed, then this sometimes leads to variations in the system specifications and this causes malfunctioning of the control system. This is the reason the control system must be redesigned. So the redesigning of control system produces accurate results by adding an external physical device is known as a compensation and the physical device added to the system is known as a compensator. This is the circuit diagram of LAC compensator. EI of t is the input signal and E0 of t is the output signal. When a sinusoidal input is applied to a network and it produces the sinusoidal steady state output having phase lag with respect to input, then such a network is called as a lag network. Generally, phase lag occurs in the low frequency region. Now derive the transfer function of LAC compensator. First apply the KVL to the input loop which consists of R1, R2 and C. So write down the equation EI of t is equal to I of t into R1 plus I of t into R2 plus 1 upon C integration of I of t dt. Now take the Laplace transform of this equation. Therefore, EI of s is equal to I of s into bracket R1 plus R2 plus 1 upon SC. This is the equation number 1. Now apply the KVL to the output port which consists of R2 and C. So E0 of t is equal to I of t into R2 plus 1 upon C integration of I of t dt. Now take the Laplace transform. So E0 of s is equal to I of s into bracket R2 plus 1 upon SC. This is equation 2. Now substitute I of s from equation 2 in equation 1 we will get. So EI of s is equal to E0 of s upon R2 plus 1 upon SC into R1 plus R2 plus 1 upon SC. Therefore E0 of s upon EI of s is equal to 1 plus SR2C divided by 1 plus SR1 plus R2 into C. Therefore, the transfer function becomes E0 of s upon EI of s is equal to 1 upon beta into s plus 1 upon t divided by s plus 1 upon beta t where t is equal to R2C and beta is equal to R1 plus R2 divided by R2. Generally beta is greater than 1. As the beta is greater than 0, the pole is located to the right half of 0. Usually beta is greater than 10. So this is the pole 0 plot. So in this transfer function, 1 0 is available at s is equal to minus 1 upon t and the 1 pole is at s is equal to minus 1 upon beta t. So this is the pole 0 plot. Now pole R plot of lag compensator. We know the transfer function of lag compensator E0 of s upon EI of s is equal to 1 plus t s divided by 1 plus beta t s. Now in frequency daemon, we get E0 of j omega divided by EI of j omega is equal to 1 plus j omega t divided by 1 plus j omega beta t. Now determine the magnitude. So magnitude is equal to under root 1 plus omega square t square divided by under root 1 plus omega square beta square t square. Now the phase angle phi is equal to tan inverse of omega t minus tan inverse of omega beta t. Now substitute the values when omega is equal to 0, the magnitude becomes equal to 1 and the phase angle is equal to 0 degree. And when we substitute omega is equal to infinity, then magnitude becomes equal to 1 upon beta and phi is equal to 0 degree. So this is the pole R plot for lag compensator. Let us see the effect of lag compensator. It allows high gain at low frequency, thus it is basically low pass filter. Hence it improves the steady state performance of the system. The bandwidth of the system gets reduced. Reduced bandwidth means slower response and rise time and settling time are usually larger. Let us see the advantages of lag compensator. A phase lag network offers high gain at low frequency, thus it performs the function of the low pass filter. The introduction of this network increases the steady state performance of the system. The lag network offers a reduction in bandwidth and this provides longer rise time and settling time and so the transient response. Disadvantages of lag compensator. In lag compensator, the attenuation offered by it shifts the gain crossover frequency to lower point thereby decreasing the bandwidth. Though the system response is longer due to decreased bandwidth, however the response is quite slow. A control system with lag network shows more sensitivity towards variation in the parameters than a system with a lead network. It provides attenuation to high frequency range. Try to give the answer of this question. Bandwidth is reduced when compensator used is lead compensator, lag compensator, lag lead compensator and none of these. So which answer is correct answer? The correct answer is lag compensator. How bandwidth of the system decreases in phase lag network? In phase lag network, the gain crossover frequency shifts to lower value. Effect of this, the bandwidth of the system decreases. These are the references. Thank you.