poles

A certain application requires power at a frequency of 16.67 Hz, while the available grid frequency is 50 Hz. A 3-phase synchronous motor connected to the 50 Hz, 3-phase grid, driv...

A system is characterized by the following state equation and output equation (U: input, X: state vector, y: output) $\dot{x} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}x + \be...

Consider the state-space model $\dot{x}(t) = Ax(t) + Br(t)$, $y(t) = Cx(t)$ where $x(t)$, $r(t)$, $y(t)$ are the state, input and output, respectively. The matrices A, B, C are giv...

Consider the state-space model $$ \begin{aligned} \dot{x}(t) & =A x(t)+B u(t) \\ y(t) & =C x(t) \end{aligned} $$ where $x(t), r(t), y(t)$ are the state, input and output, respectiv...

If C is a circle $|z| = 4$ and $f(z) = \frac{z^2}{(z^2-3z+2)^2}$, then $\oint_C f(z)dz$ is

Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H(1) = $\frac{5}{4}$. The poles of...

A discrete system is represented by the difference equation $$$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a-1\\a+1&a\end{bmatrix}\begin{b...

Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be

A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce power at $$50$$ $$Hz,$$ the number of poles required in the g...

The system represented by the transfer function $$G\left( s \right) = {{{s^2} + 10s + 24} \over {{s^4} + 6{s^3} - 39{s^2} + 19s + 84}}$$ has . . . pole $$(s)$$ in the right-half $$...

The Laplace transformation of f(t) is F(s). Given F(s)=$$\frac\omega{s^2+\omega^2}$$, the final value of f(t) is