 Hello, myself Sunil Kalshati, assistant professor, Department of Electronics Engineering, Walchand Ishwap Technology, Swalapur. Today, I am going to discuss the LEAD compensator. Learning outcome. At the end of this session, students can analyze LEAD compensator, compensation of control system. Let us see the definition of compensation. LEAD design or alteration of system using an additional device is called as a compensation of control system compensator. An external device which is used to alter the behavior of the system so as to achieve the given specification is called as a compensator. What is the necessity of the compensation? In order to obtain the desired performance of the system, we have to use the compensating networks. Compensating networks are applied to the system in the form of feed forward path gain adjustment. Compensate an unstable system to make it stable. A compensating network is used to minimize the overshoots. These compensating networks increases the steady state accuracy of the system. An important point to be noted here is that the increase in steady state accuracy brings the instability to the system. Compensating networks also introduces poles and zeros in the system thereby causes changes in the transfer function of the system. Due to this, the performance of the system changes. Types of compensation. Basically, there are three types of compensation. Series compensation, parallel compensation and third series and parallel compensation. So, this is the block diagram of series compensation. Here g of s is the transfer function of the forward path, h of s is the transfer function of the feedback path and g c of s is the transfer function of the compensator which is connected in series that is why this is the transfer function for the series compensator. It is also called as a cascade connection. In this scheme, the flow of signal is from lower energy level towards to higher energy level. This required additional amplifier to increase the gain. The number of components required in series scheme is more than in the parallel scheme. Let us see the parallel compensation. This is the block diagram of parallel compensation. Already we know what is the g of s and what is the h of s? g of s, g of s is the transfer function of the forward path and h of s is the transfer function of the feedback path and here g c of s is the transfer function of the compensator which is connected in parallel. It is also called as a cascade connection. In this scheme, the flow of signal is from lower energy level towards to higher energy level. This required additional amplifier to increase the gain. The number of components is required in series scheme is more than in the parallel scheme. Let us see the series parallel compensation. So this is the block diagram of the series parallel compensation. Here g c of, g c 1 of s is the transfer function of series compensator. g c 2 of s is the transfer function of parallel compensator to provide both series as well as parallel compensation and as well as feedback. Such a scheme is used and such a scheme is called as a series parallel compensation. The selection of proper compensation scheme depends on the nature of signals available in the system and power levels at various points. Let us see compensating networks. Basically there are three types of compensating networks. Lead compensator, it is also called as a lead network. Lag compensation compensator and lead lag compensator. Lead compensator. This is the circuit diagram for the lead compensator. Here e i of t is the input signal and e 0 of t is the output signal. Then sinusoidal input is applied to network and it produces sinusoidal steady state output having phase lead with respect to input. Then a network is called as a lead network. Generally phase lead occurs in the high frequency region. Lead compensator required to improve the transient response of the system. Bandwidth is increased when lead compensator is used. The phase lead compensation is used to decrease the rise time and overshoot. Now derive the transfer function for lead compensator. As we know the transfer function means the Laplace transform of output to the Laplace transform of input. So, e 0 of s upon e i of s is equal to s plus 1 upon r 1 into c divided by s plus r 1 plus r 2 divided by r 1 r 2 c. Now simplify this equation. Therefore the expression becomes e 0 of s upon e i of s is equal to s plus 1 upon t divided by s plus 1 upon alpha t. Now substitute t is equal to r 1 c and alpha is equal to r 2 upon r 1 plus r 2. Therefore the transfer function becomes e 0 of s upon e i of s is equal to s plus 1 upon t divided by s plus 1 upon alpha t. Now in this transfer function 1 0 is present at s is equal to minus 1 upon t and another pole is present at s is equal to minus 1 upon alpha t. So this is the pole 0 diagram for the lead compensator. Here in this transfer function alpha is greater than 0 and less than 1. Therefore the 0 is always located to the right half of pole. Now polar plot of lead compensator as we know the transfer function of lead compensator is alpha into bracket 1 plus ts divided by 1 plus alpha ts. Now replace s by j omega therefore e 0 of j omega divided by e i of j omega equal to alpha into bracket 1 plus j omega t divided by 1 plus j omega alpha t. Now determine the magnitude therefore magnitude becomes equal to alpha into bracket under root 1 plus omega square t square divided by under root 1 plus omega square alpha square t square while the phase angle is given by phi is equal to tan inverse of omega t minus tan inverse omega alpha t. Now substitute omega is equal to 0 when we substitute omega is equal to 0 then magnitude becomes alpha and phi is equal to 0 and when we substitute omega is equal to infinity then the magnitude becomes equal to 1 and phi becomes 0 degree. This is the polar plot for the lead compensator. Now the compensator required to improve the transient response of the system options are lead compensator, lag compensator, lag lead compensator and none of these. So which answer is correct answer? So the correct answer is the lead compensator advantages of phase lead compensation. Due to the presence of phase lead network the speed of the system increases because of it the gain crossover frequency shifts to higher value. Due to the presence of phase lead compensation maximum overshoot of the system decreases. How bandwidth of system increases in phase lead network? Due to the phase lead network the gain crossover frequency shifts to higher value effect of this the bandwidth of the system increases. These are the references. Thank you.