 Hello, myself, Sunil Kalshatti, assistant professor, Department of Electronics Engineering, Walchan, Institute of Technology, Swalapur. Today, I am going to discuss the proportional controller, learning outcome. At the end of this session, students can analyze the proportional controllers. Let us see, what is the controller? A controller is a mechanism that seeks to minimize the difference between the actual value of the system and the desired value of the system. It is the difference between the actual value of the system, means process variable and the desired value of the system means set point. Controls are a fundamental part of control engineering and used in all the complex control system. A controller is a device introduced in a feedback path or in the forward path of the system. It controls the steady state and the transient response as per the requirement. In most of the practical system, controller output is proportional to the error generated, the important uses of the controllers. Controllers improve the steady state accuracy by decreasing the steady state error. As the steady state accuracy improves, the stability also improves. Controllers also helps in reducing the unwanted offsets produced by the system. Controllers can control the maximum overshoot of the system. Controllers can help in reducing the noise signals produced by the system. Controllers can help to speed up the slow response of an over-damped system. Let us see types of controllers. Basically, there are two types of controllers. One is continuous controller, another is the discontinuous controller. In discontinuous controller, the manipulated variable changes between the discrete values. Depending on how many different states the manipulated variable can assume, a distinction is made between the two position, three position and multi-position controllers. As compared to continuous controller, discontinuous controllers operates on very simple switching final controlling elements, continuous controllers. The main feature of the continuous controllers is that controlled variable means manipulated variable can have any value within the controller's output range. Now in the discontinuous control theory, there are three basic modes on which the whole control action takes place. So first one is the proportional controllers, second one integral controllers, third one derivative controllers. We use the combination of these modes to control our system such that the process variable is equal to the set point. These three types of controllers can be combined into new controllers, proportional and integral controller, PI controller. It is the combination of proportional and integral controller, proportional and derivative controller, PD controller and combination of proportional, integral and derivative forms the PID controller, proportional, integral, derivative controller, proportional controller. control in engineering is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value and measured value. Desired value means set point value. The proportional controller produces an output which is proportional to the error signal. So, E of t is directly proportional to E of t, where E of t is the output signal and E of t is the error signal. So, E of t is equal to K p into E of t. Now, apply the Laplace transform on both side. Therefore, E of s is equal to K p into E of s. Now, here E of s upon E of s is equal to K p. So, it acts as a transfer function of the proportional controller where K p is also called as a proportionality constant. Now, here E of s is the Laplace transform of actuating signal E of t. E of s is the Laplace transform of error signal and K p is the transfer function of the proportional controller. It is also called as a proportionality constant. This is the block diagram of proportional controller. The block diagram of the unity negative feedback closed loop system along with proportional controller is as shown above. Here, R of s is the reference input signal and C of s is the controlled output signal. We will derive the transfer function. Consider such a second order system where the controller input is the error itself and the proportionality constant is 1. Therefore, G of s H of s is equal to omega n square divided by s into bracket s plus 2 zeta omega n. Therefore, C of s upon R of s is equal to 1 upon 1 plus G of s H of s. Therefore, omega n square divided by s square plus 2 zeta omega n s plus omega n square. For this system, damping ratio is zeta and natural frequency is omega n. And for the steady state error, K p is equal to limit s tends to 0, G of s H of s is equal to infinity and K v is equal to limit s tends to 0 as G of s H of s is equal to omega n upon 2 zeta. Therefore, steady state error E s s is equal to A upon 1 plus K p, steady state error E s s is equal to A upon K v. Now, if transient response is improved, damping ratio must be changed. In general, good time response demands less settling time, less overshoots, less rise time and smallest steady state error by increasing K v that is increases in the steady state gain. Steady state error can be reduced, but due to high settling time and peak overshoot increases. This may lead to instability of the system. So, try to give the answer of this question. Controllers improve the steady state accuracy option A by decreasing the steady state error, by increasing the steady state error, by maintaining constant steady state error D none of the bow. So, which option is correct option? The correct option is A by decreasing steady state error, advantages of proportional controller. The proportional controller helps in reducing the steady state error thus makes the system more stable. The slow response of the over damped system can be made faster within the help of these controllers. Due to the presence of these controllers, we get some offset in the system. Proportional controllers also increases the maximum overshoot of the system. These are the references. Thank you.