Routh-Hurwitz stability criterion is an analytical method used for the determination of stability of a linear time-invariant system. The basis of this criterion revolves around simply determining the location of poles of the characteristic equation in either left half or right half of s-plane despite solving the equation. We have already discussed, the stability of the control system in our previous article. It is considered an important parameter of the control system. The stability of a … [Read more...] about Routh-Hurwitz Stability Criterion

# Control Systems

## Nyquist Stability Criterion

Nyquist criterion or Nyquist stability criterion is a graphical method which is utilized for finding the stability of a closed-loop control system i.e., the one with a feedback loop. This criterion serves as a crucial way for design and analysis purpose of the system with feedback. Thus, it finds major application in Electronics and Control System Engineering. The principle of Nyquist criterion was independently proposed by an electrical engineer of German origin, Felix Strecker in the year … [Read more...] about Nyquist Stability Criterion

## Observability

Observability of a control system is the ability of the system to determine the internal states of the system by observing the output in a finite time interval when input is provided to the system. It is another crucial property of the control system as it shows the behavioural approach of the control system. It is also proposed by R. Kalman, the one who proposed controllability. Observability in control system For a better understanding of the term observability, let us understand it in … [Read more...] about Observability

## Controllability

Controllability is defined as the ability of a control system to reach a definite state from a fixed (initial) state in a finite time. It is considered as an important property of the control system as it defines the behaviour of the control system. The theory of controllability was proposed in 1960 by R. Kalman. Controllability in Control System A system is completely controllable if the initial state of the system is transferred to any particular state, in a finite time duration, when a … [Read more...] about Controllability

## Lag Lead Compensator

Definition: A lag lead compensator is a type of electrical network that generates phase lag as well as phase lead in the output signal at different frequencies when a steady-state sinusoidal input is provided to it. It is also known as lag lead network. In case of a lag lead compensator, the phase lead and phase lag occur at different frequency regions. Generally, at low-frequency phase lag characteristics is noticed in the output of the circuit. While at high frequency, we have phase lead … [Read more...] about Lag Lead Compensator

## Lag Compensator

Definition: A lag compensator is a circuit that is designed to generate a steady-state sinusoidal signal having a phase lag to the applied input sinusoidal signal. This can also be stated in a way that it is a circuit that is when provided with a sinusoidal input produces a sinusoidal output signal whose phase lags the applied input. It is sometimes referred as a lag network. We know that compensators are used in the control system in order to have the desired output. Basically, the … [Read more...] about Lag Compensator

## Lead Compensator

Definition: A lead compensator is an electrical circuit that when provided with a sinusoidal input generates a sinusoidal signal as output with a phase lead in comparison to that of the applied sinusoidal signal. It is also known as lead network. What is compensator? We are aware of the fact that control systems are used to control the behaviour of the system in order to provide the desired output. But for proper controlling, the control system must also be properly designed. The major … [Read more...] about Lead Compensator

## Time Response of Second Order System

The type of system whose denominator of the transfer function holds 2 as the highest power of ‘s’ is known as second-order system. This simply means the maximal power of ‘s’ in the characteristic equation (denominator of transfer function) specifies the order of the control system. The order of the system provides the idea about closed-loop poles of the system. The block diagram of the second-order system with unity feedback is given below: Introduction We have already discussed in … [Read more...] about Time Response of Second Order System

## State Space Analysis

State Space analysis (also known as state variable analysis) is a commonly used method nowadays for analyzing the control system. The analysis that involves providing a complete idea about the behavior of the system at any given time utilizing the history of the system is known as state-space analysis. The analysis of the control system in this approach is based on the state of the system. Thus it is called so. We know that the basic method used to analyze the control system is a transfer … [Read more...] about State Space Analysis

## Time Response of First Order System

The type of system having ‘1’ as the maximum power of ‘s’ in the denominator of the transfer function of the control system is known as the first-order system. Thus, we can say, that the order of the system is specified by the highest power of s. Basically the order of the system shows information regarding the closed-loop poles of the system. Thus for the first-order system, we can say that there will be one closed-loop pole. Here we can see the block diagram of unity negative feedback … [Read more...] about Time Response of First Order System