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Are the given plant transfer function stable or unstable?
The plant transfer function G(s) is shown below: The complete closed-loop transfer function, including the proportional controller Kp, is: Answer: No proportional controller gain can make the system stable since the closed-loop transfer function has zero “s” and “s2” term coefficients.
What makes a system stable?
A system is said to be stable, if its output is under control. Otherwise, it is said to be unstable. A stable system produces a bounded output for a given bounded input. Therefore, the first order control system is stable since both the input and the output are bounded.
What is the stability of a control system?
What is Stability? A system is said to be stable, if its output is under control. Otherwise, it is said to be unstable. A stable system produces a bounded output for a given bounded input. The following figure shows the response of a stable system.
How is the stability of a transfer function determined?
Transfer function stability is solely determined by its denominator. The roots of a denominator are called poles. Poles located in the left half-plane are stable while poles located in the right half-plane are not stable. The reasoning is very simple: the Laplace operator “s”, which is location in the Laplace domain, can be also written as:
What does k mean for transfer function gain?
K represents the transfer function gain, irrespective of the order of the function. Every control system designer aims for a stable system, since stability is an important factor for a system to behave as expected.
How to find the gain of the transfer function?
With this knowledge, just consider a first-order system, with transfer function: The transfer function gain is obtained as K, substituting s=0. So the transfer function is given in the form: where N (s) and D (s) are the numerator and denominator polynomials respectively.
Which is the magnitude of the transfer function?
The transfer function gain is the magnitude of the transfer function, putting s=0. Otherwise, it is also called the DC gain of the system, as s=0 when the input is constant DC. If Ka is the given transfer function gain and Kc is the gain at which the system becomes marginally stable, then GM=KcKa