Time Domain Analysis part1 -2.pdf

Time Domain Analysis of Control Systems Chapter 5 Automatic Control System, Kuo 9thEdition Dr. Mohammed Obaid Mustafa Department of Electrical Eng. University of Mosul 7-05/2023  The time response of a control syst...

Time Domain Analysis of Control Systems Chapter 5 Automatic Control System, Kuo 9thEdition Dr. Mohammed Obaid Mustafa Department of Electrical Eng. University of Mosul 7-05/2023  The time response of a control system is usually divided into two parts: the transient response and the steady-state response. Let y(t) denote the time response of a continuous data system; then, in general, it can be written as Where: Yi (t) denotes the transient response Yss (t) denotes the steady-state response.  TYPICAL TEST SIGNALS FOR THE TIME RESPONSE OF CONTROL SYSTEMS Step-Function Input The mathematical representation of a step function or magnitude R is Ramp Function Input: The ramp function is a signal that changes constantly with time. Mathematically, a ramp function is represented by where R is a real constant Parabolic-Function Input: The parabolic function represents a signal that is one order faster than the ramp function. Mathematically, it is represented as The maximum overshoot is often used to measure the relative stability of a control system.  STEADY-STATE ERROR The difference between the output and the reference in the steady state was defined earlier as the steady-state error. The three terms in the denominator that are taken to the limit determine the steady-state error. We call these limits static error constants. Individually, their names are Ex: For the following system, evaluate the static error constants and find the expected error for the standard step, ramp, and parabolic inputs SOLUTION: Relationships between input, system type, static error constants, and steady- state errors How can find Ess from state space? Steady-State Error for Nonunity Feedback Systems Ex: find the system type, the appropriate error constant associated with the system type, and the steady-state error for a unit step input. Assume input and output units are the same. The negative value for steady-state error implies that the output step is larger than the input step.