Free Expert Guides on Power Systems, Circuit Design & Electrical Troubleshooting

What is Steady State Error?Steady State Error DefinedSteady state error is the discrepancy between a control system’s desired and actual output values once the output has stabilized.Influence of Input TypesThe size of the steady state error varies with different types of inputs—zero for step inputs, a constant for ramp inputs, and infinite for parabolic inputs.System StabilityUnlike steady state error, the stability of a control system does not depend on the type of input but on the system’s tra

What is a Transfer Function?DC Gain DefinitionDC gain is the ratio of the steady-state output to the steady-state input of a control system when given a step input.Transfer FunctionA transfer function represents the relationship between a control system’s input and output using the Laplace transform.Final Value TheoremThe final value theorem helps find the DC gain by evaluating the transfer function at zero for continuous systems.Continuous vs. Discrete SystemsDC gain calculations differ between

What is Rise Time?Rise Time DefinitionRise time is defined as the duration it takes for a signal to increase from 10% to 90% of its steady value, indicating how quickly a signal changes.Rise Time FormulaThe rise time formula varies based on the system type.Calculation MethodTo calculate rise time, use the transfer function to determine time constants and calculate the times when the signal reaches 10% and 90% of its final value.Practical MeasurementRise time is typically measured using an oscill

We have already discussed the Fourier series in exponential form. In this article we will discuss another form of Fourier series i.e. Trigonometric Fourier series.Fourier series representation in Trigonometric formFourier series in trigonometric form can be easily derived from its exponential form. The complex exponential Fourier series representation of a periodic signal x(t) with fundamental period To is given bySince sine and cosine can be expressed in exponential form. Thus by manipulating t

Fourier Series at a GlanceA continuous time signal x(t) is said to be periodic if there is a positive non-zero value of T for whichAs we know any periodic signal can be classified into harmonically related sinusoids or complex exponential, provided it satisfies the Dirichlet’s Conditions. This decomposed representation is called FOURIER SERIES.Two type of Fourier Series representation are there. Both are equivalent to each other. Exponential Fourier Series Trigonometric Fourier SeriesBoth repres

Sometimes all the information in time domain is not sufficient. This makes us to move to frequency domain of the signal for extracting more information about the signal. This movement from one domain to other domain is known as transformation. For changing the domain of signal from time to frequency we have many tools. Fourier Series and Fourier Transform are two of the tools in which we decompose the signal into harmonically related sinusoids. With such decomposition, a signal is said to be rep

In a control system, there may be some energy storing elements attached to it. Energy storing elements are generally inductors and capacitors in case of an electrical system. Due to the presence of these energy storing elements, if the energy state of the system is disturbed, it will take a certain time to change from one energy state to another. The exact time taken by the system for changing one energy state to another is known as transient time and the value and pattern voltages and currents

What is a Nichols Chart?A Nichols Chart (also known as a Nichols Plot) is a plot used in signal processing and control system design to determine the stability and closed-loop frequency response of a feedback system. The Nichols chart is named after its founder, Nathaniel B. Nichols.How Does A Nichols Chart Work?Constant magnitude loci that are M-circles and constant phase angle loci that are N-circles are the fundamental components in designing the Nichols chart.The constant M and constant N ci

Laplace transformation is a technique for solving differential equations. Here differential equation of time domain form is first transformed to algebraic equation of frequency domain form. After solving the algebraic equation in frequency domain, the result then is finally transformed to time domain form to achieve the ultimate solution of the differential equation. In other words it can be said that the Laplace transformation is nothing but a shortcut method of solving differential equation.In

What is a Nyquist Plot?A Nyquist plot (or Nyquist Diagram) is a frequency response plot used in control engineering and signal processing. Nyquist plots are commonly used to assess the stability of a control system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the X-axis, and the imaginary part is plotted on the Y-axis.The frequency is swept as a parameter, resulting in a plot based on frequency. The same Nyquist plot can be described using polar c