Parseval’s theorem Proof

In this article, we will see Parseval’s theorem proof. Before we go any further, first learn What is Parseval’s theorem? It states that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. Parseval’s theorem is also known as Rayleigh’s energy theorem or Rayleigh’s Identity … Read more

Controllers | Proportional, Integral & Derivative Controllers

In control engineering, characterization of a controlled system is primarily determined by its dynamic behaviour which also characterizes the scope and the quality needed to solve a control task. The step response of the controlled system is used to reflect this dynamic behaviour. A controller is one of the most important parts of the control … Read more

Control System Basics

Our daily activities are getting automated every day. Control System plays an important role in making our life automated and modernized. A microwave, refrigerator, an air conditioner, a geezer, an automatic iron, are some examples of a control system. Many engineering fields use control system principle in many applications.   System It is an interconnection … Read more

Proportional-Integral (PI) Controllers

Proportional-Integral (PI) controllers are used in many industrial control applications. The main purpose of using Proportional and Integral (PI) in process system is to improve the steady-state accuracy of the system without affecting the stability of the system. Proportional action responds quickly to the error deviation and the integral action will act slowly but offset … Read more

Frequency Domain Analysis | Advantages

Frequency Response The Frequency Response of the system is the steady-state response of the system obtained as the output when a sinusoidal input signal is given to the system. For determining the frequency response of a control system sinusoidal signal is given as input to the system with different frequencies and response of the output … Read more

Proportional (P), Integral (I), Derivative (D) Controllers Usage Conditions

1. When does the Proportional (P) Controller is used? Answer. Proportional (P) Controller is used during the following conditions: Load Changes are small Offset (error exist due to difference between steady state value and desired value) can be tolerated. The process reaction rate is such as to permit a narrow proportional band. Since this reduces … Read more

Extended Kalman Filter | Algorithm & Applications

In the previous article, we had learned about Kalman filter. As Kalman filter assumes linear system but finds greatest applications in non-linear systems. Kalman filter assumes an approximate solution, describe the deviations from the reference by linear equations. Kalman filter has issues of divergence also. When the error covariance matrix Pk computed by the Kalman filter … Read more

Kalman Filter | Algorithm & Applications

The Kalman filter is a recursive state space model based estimation algorithm. In other words, it is an optimal recursive data processing algorithm. Kalman filter is also called as the Predictor-Corrector algorithm. This filter is named after Rudolph E. Kalman, who in 1960 published his famous paper describing a recursive solution to the discrete data … Read more

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