Nyquist Stability Criterion is a graphical method used in control-system analysis to determine the closed-loop stability of a feedback system by examining how the frequency response of the open-loop transfer function G(s)H(s)G(s)H(s) encircles the critical point (−1, 0)(-1,\,0) in the complex plane.It is based on the Nyquist plot and relates the number of encirclements of the […]
Category: Control Systems
Bode Plot
Bode Plot is a graphical method used in control-system analysis to represent the frequency response of a system using two plots: the magnitude plot, which shows the gain (in decibels, dB) versus frequency, and the phase plot, which shows the phase angle (in degrees) versus frequency, both typically plotted against a logarithmic frequency scale. A […]
Root Locus
Root Locus is a graphical method used in control system analysis to show how the closed-loop poles of a system move in the complex plane as the system gain KK varies from zero to infinity. It is based on the characteristic equation 1+KG(s)H(s)=01+KG(s)H(s)=0 and helps engineers study system stability, transient response, damping, natural frequency, and […]
Derivative (D) Control
Derivative (D) Control is a control method in which the controller output is proportional to the rate of change of the error with time. It is expressed as u(t) = Kd de(t)/dt, where u(t) is the controller output, e(t) is the error, and Kd is the derivative gain. By responding to how quickly the error […]
Integral (I) Control
Integral (I) Control is a control method in which the controller output is proportional to the accumulated error over time. It is expressed as u(t) = Ki ∫e(t)dt, where u(t) is the controller output, e(t) is the error, and Ki is the integral gain. By continuously accumulating past errors, integral control can eliminate or significantly […]
Proportional (P) Control
Proportional (P) Control is a control method in which the controller output is directly proportional to the present error between the desired setpoint and the actual system output. It is expressed as u(t) = Kp e(t), where u(t) is the controller output, e(t) is the error, and Kp is the proportional gain. Increasing Kp generally […]
Impulse Response
Impulse Response is the response of a control system when the input is a unit impulse signal, represented by r(t)=δ(t)r(t)=\delta(t) in the time domain and R(s)=1R(s)=1 in the Laplace domain. It is an important way to study the transient behavior, stability, natural dynamics, and speed of response of a system. For a system with transfer […]
Ramp Response
Ramp Response is the response of a control system when the input increases linearly with time, typically represented by a unit ramp input r(t)=tr(t)=t and R(s)=1/s2R(s)=1/s^2. It is used to evaluate how effectively a control system can track a continuously changing reference signal. The ramp response helps analyze transient behavior, tracking accuracy, steady-state error, rise […]
Step Response
Step Response is the response of a control system when the input changes suddenly from zero to a constant value, typically represented by a unit step input R(s)=1/sR(s)=1/s. It is one of the most commonly used methods for analyzing the time-domain performance of a control system. The step response shows how the system output changes […]
Steady-State Error
Steady-State Error is the difference between the desired input and the actual output of a control system after the transient response has disappeared and the system has reached its steady operating condition. It is commonly expressed as ess=limt→∞e(t)e_{ss}=\lim_{t\to\infty}e(t), and it indicates the accuracy of the system in following a reference input. A smaller steady-state error […]