PYQs Based Test - 05 : Control Systems

The complete Nyquist plot of the open-loop transfer function G(s) H(s) of a feedback control system is shown in the figure.



If G(s) H(s) has one zero in the right-half of the s-plane. the number of poles that the closed-loop system will have in the right-half of the s-plane is

A unity feedback system that uses proportional-integral (PI) control is shown in the figure.



The stability of the overall system is controlled by tuning the PI control parameters K${}_P$ and K${}_I$. The maximum value of K${}_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ________.

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function $H\left(s\right)=\frac{Y\left(s\right)}{X\left(s\right)}$ is

Consider the state space realization

≤ft[ {*20c {x_1≤ft( t )}\\ {x_2≤ft( t )} } ] = ≤ft[ {*20c 0&0\\ 0& - 9 } ]≤ft[ {*20c x_1≤ft( t )\\ x_2≤ft( t ) } ] + ≤ft[ {*20c 0\\ 45 } ]u≤ft( t ), with the initial condition ≤ft[ {*20c x_1≤ft( 0 )\\ x_2≤ft( 0 ) } ] = ≤ft[ {*20c 0\\ 0 } ].

where u(t) denotes the unit step function. The value of

$\underset{t\to \infty }{\lim }\left|\sqrt{x_1^2\left(t\right)+x_2^2\left(t\right)}\right|$ is ________.

The open loop transfer function $G\left(s\right)=\frac{\left(s+1\right)}{s^p\left(s+2\right)\left(s+3\right)}$

Where p is an integer, is conducted in unity feedback configuration as shown in the figure.



Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is______.