Recent activity in Control Systems

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Statement for Linked Answer Questions $82a$ and $82b:$The dopen loop transfer function of a unity feedback system is given by\[\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}\]Base...
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The asymptotic magnitude Bode plot of a minimum phase system is shown in thefigure. The transfer function of the system is $(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}$, where ...
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Consider the differential equation $\dot{\vec{w}}=A \vec{w}$, with $\vec{w}(t=0)=\left[\begin{array}{l}1 \\ 1\end{array}\right]$. If $\vec{w}(t)=e^{t} \vec{u}_{x}+e^{-2 t...
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Consider the system shown in the figure is. Determine the value of a such that the damping ratio is $0.5$. Also obtain the values of the rise time $t_{r}$ and maximum ove...
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If the Laplace transform of a signal $y(t)$ is $Y(s)=\dfrac{1}{s(s-1)},$ then its final value is$-1$$0$$1$Unbounded
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The open loop transfer function of a feedback control system is:$$ G(s) H(s)=\frac{1}{(s+1)^3} $$The gain margin of the system is:$2$$4$$8$$16$
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Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the thre...
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A certain system has transfer function $G(s)=\dfrac{s+8}{s^{2}+\alpha s-4}$, where $\alpha$ is a parameter. Consider the standard negative unity feedback configuration as...
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Consider the unity negative feedback control system shown in the Figure.The value of gain $K(>0)$ at which the given system will remain marginally stable is $\_\_\_\_$.(A...
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The state and output equations for a control system are:\[\begin{array}{c}\dot{x}=\left[\begin{array}{cc}-4 & -1.5 \\4 & 0\end{array}\right] x+\left[\begin{array}{l}2 \\0...
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For the control system shown in the Figure, the transfer function of a plant, $G(s)=\frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s)=K(s+\alpha)$, w...
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A control system is shown in the Figure.Which option represents the correct transfer function of the system?$\dfrac{1}{(s+4)^{2}}$$\dfrac{1}{(s+4)}$$\dfrac{2}{(s+4)}$$\df...
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Consider a system where $x_{1}(t), x_{2}(t)$, and $x_{3}(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the sys...
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The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system in the figure.If $G(s)H(s)$ has one zero in the right-half of the $s$...
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The Nyquist plot of a system is given in the figure below. Let $\omega_{P}, \omega_{Q}, \omega_{R}$, and $\omega_{S}$ be the positive frequencies at the points $\boldsymb...
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For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is$16$$4$$2$$1$
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The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state transition matrix $e^{At}$ ...
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A ramp input applied to an unity feedback system results in $5 \%$ steady state error. The type number and zero frequency gain of the system are respectively$1$ and $20$$...
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Consider a system with the transfer function $G(s)=\frac{s+6}{k s^2+s+6}$. Its damping ratio will be $0.5$ when the value of $k$ is$2 / 6$$3$$1 / 6$$6$
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​​​​​A satellite attitude control system, as shown below, has a plant with transfer function $G(s)=\frac{1}{s^{2}}$ cascaded with a compensator $C(s)=\frac{K(s+\alpha)}{s...
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​​​​​Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown.The impulse response of the closed-loop system dec...
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Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).
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Consider the polynomial $p(s)=s^{5}+7 s^{4}+3 s^{3}-33 s^{2}+2 s-40$. Let $(L, I, R)$ be defined as follows.$L$ is the number of roots of $p(s)$ with negative real parts....
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Let $G(s)=\frac{1}{10 s^{2}}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below.Co...
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Consider the unity-negative-feedback system shown in Figure $(i)$ below, where gain $K \geq 0$. The root locus of this system is shown in Figure $(ii)$ below.For what val...
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Consider the system shown below.If $K>0$, which of the following describes the system?Stable, causalStable, non-causalUnstable, non-causalUnstable, causalCannot be determ...
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Consider a system which in response to input $x(t)$ outputs\[y(t)=2 x(t-2)+x(2 t-1)+1 .\]Which of the following describes the system?linear, time-invariant, causallinear,...
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Consider a system which in response to input $x(t)$ outputs\[y(t)=x\left(t^{2}\right) .\]Which of the following describes the system?linear, time-invariant, causallinear,...
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For a time-invariant system, the impulse response completely describes the system if the system iscausal and non-linearnon-causal and non-linearcausal and linearAll of th...
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A linear time-invariant system has a transfer function $H(s)=1 /(1+s)$. If the input to the system is $\cos (t)$, the output is$\left(e^{j t}+e^{-j t}\right) / 2$ where $...
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