GATE EE
Control Systems
Routh Hurwitz Stability
Previous Years Questions

## Marks 1

The open loop transfer function of a unity gain negative feedback system is given by $$G(s) = {k \over {{s^2} + 4s - 5}}$$. The range of k for which t...
A closed loop system has the characteristic equation given by $${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, whi...
A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$𝐻(𝑠).$$ It is given that $$\l... In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicate... The first two rows of Routh's tabulation of a third order equation are as follows$$$\left. {\matrix{ {{s^3}} \cr {{s^2}} \cr } } \right|\... The system shown in the figure is ... None of the poles of a linear control system lie in the right half of $$s$$-plane. For a bounded input, the output of this system Closed loop stability implies that $$\left[ {1 + G\left( s \right)H\left( s \right)} \right]$$ has only ____________ in the left half of the $$s$$-pla... The number of positive real roots of the equation $${s^3} - 2s + 2 = 0$$ is __________. The closed loop system , of Figure, is stable if the transfer function $$T\left( s \right) = {{C\left( s \right)} \over {R\left( s \right)}}$$ is stab... For what range of $$K$$ is the following system (Figure) asymptotically stable Assume $$K \ge 0$$ ... ## Marks 2 The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the complex $$s$$-plane is Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which have real parts strictly less ... The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator w... A system with the open loop transfer function $$G\left( s \right) = {K \over {s\left( {s + 2} \right)\left( {{s^2} + 2s + 2} \right)}}$$ is connected ... For the given system, it is desired that the system be stable. The minimum value of $$\alpha$$ for this condition is _________ ... The feedback system shown below oscillates at $$2$$ rad/s when ... Figure shows a feedback system where $$K>0$$ The range of $$k$$ for which system is stable will by given by... If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {s + 8} \right)^2}$$ is to be a... The algebraic equation $$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$ $$F\left( s \right) = 0$$ has For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {1 - s} \right)} \over {\left( ... The loop gain$$GH$$of a closed loop system is given by the following expression$${K \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$The ... The number of roots on the equation$$2{s^4} + {s^3} + 3{s^2} + 5s + 7 = 0$$that lie in the right half of$$S$$plane is: The system represented by the transfer function$$G\left( s \right) = {{{s^2} + 10s + 24} \over {{s^4} + 6{s^3} - 39{s^2} + 19s + 84}}$\$ has . . . pol...
Determine whether the system given by the block diagram of Figure, is stable ...
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