The objective of this book is the estimation of the levels of a quadruple tank system by using the help of kalman filter and optimal controlling the levels of the tank system is done using Linear Quadratic Regulator(LQR). Quadruple tank system is a novel multivariable process and has been widely used in control literature to illustrate many concepts in multivariable control, particularly, performance limitations due to multivariable right half-plane zeros. Estimation of the state of a system is done by utilizing the knowledge of system, measurement dynamics and assumed statistics of system noises and measurement errors and initial condition information. Kalman filter is an efficient estimator that estimates the accurate level of the quadruple tank system even from a series of noisy measurements. This optimal control strategy in which kalman filter together with linear quadratic regulator is known as Linear Quadratic Gaussian System(LQG).