FIRST and SECOND ORDER SYSTEMS
- Control Systems Engineering, Norman Nise
- Introduction Chapter 4 pp 162 (162)
- Poles and Zeros 4.1 pp 162 –
- First Order System 4.3 pp 165-168
- Second Order System 4.4 pp 168-177
- Introduction Chapter 5 pp 219 (232)
- First Order Systems 221 (234)-224
- Second Order System pp 225(238)-229
TIME DOMAIN CONTROL SYSTEMS ANALYSIS
Analisis de sistemas de control en el dominio del tiempo
FIRST ORDER SYSTEMS
We now discuss first-order systems without zeros to define a performance specification for such a system…
We now use Eqs. (4.6), (4.7), and (4.8) to define three transient response performance specifications:
- Time Constant: We call 1/a the time constant of the response. From Eq. (4.7), the time constant can be described as the time for to decay to 37% of its initial value. Alternately, from Eq. (4.8) the time constant is the time it takes for the step response to rise to 63% of its final value.
The reciprocal of the time constant has the units (1/seconds), or frequency. Thus, we can call the parameter a the exponential frequency. Thus, the time constant can be considered a transient response specification for a first order system, since it is related to the speed at which the system responds to a step input.Since the pole of the transfer function is at a, we can say the pole is located at the reciprocal of the time constant, and the farther the pole from the imaginary axis, the faster the transient response.
- Rise Time (Tr): Rise time is defined as the time for the waveform to go from 0.1 to 0.9 of its final value.
- Settling Time (Ts): Settling time is defined as the time for the response to reach, and stay within, 2% of its final value.2
Literature Review by: Larry Francis Obando – Technical Specialist
Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.
Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.
Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.
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