B.TECH - Semester 8 advanced control theory Question Paper 2008 (may)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- What are the advantages of state space approach?
- List the properties of state transition matrix.
- Define controllability of a linear time invariant system.
- What is the significance for the eigen values of a system matrix?
- With a block schematic, explain different parts of a sampled data control system.
- Explain Shannon's Sampling theorem.
- Write the mathematical expression for an impulse function. What is its Ztransform?
- Explain any two characteristics of a non-linear system.
- Write note on any two types of non-linearity.
- Check the definiteness of the Lyapunov function $V(x, y)=x^{2}+y^{2}$. ( $10 \times 4=40$ Marks) P.T.O. PART - B
- (a) Compare and contrast state space approach with classical approach.
- (b) With the help of illustrations, explain the concept of state, state space and state trajectory.
- Obtain a state space model in phase variable form of a system with transfer function $\frac{Y(s)}{U(s)}=\frac{1}{s^{3}+7 s^{2}+8 s+2}$.
- (a) If the transfer function is given in $s$-domain, $G(s)$, what are the steps involved in finding the $\mathbf{z}$-domain transfer function $G(z)$.
- (b) Given $G(s)=\frac{1}{s+2}$. Find $G(z)$.
- Consider a system represented by the difference equation $y(k)+0.9 y(k-1)=u(k)$. (a) Given $y(0)=0$. Find pulse transfer function.
- Consider a system represented by the difference equation $y(k)+0.9 y(k-1)=u(k)$. (b) Find impulse response.
- Consider a system represented by the difference equation $y(k)+0.9 y(k-1)=u(k)$. (c) Is the system stable. N - 6618
- (a) Draw the characteristic of the nonlinearity defined below where $u$ is the output of the nonlinearity and $e$ is the input. $$ \begin{aligned} u=N(e) & =-2 \text { if } e<-1 \\ & =0 \text { if }-1<e<1 . \\ & =2 \text { if } e>1 \end{aligned} $$
- (b) If the input wave form $e(t)=0.5 \sin (314 t)$ sketch the output waveform.
- (c) Mention the steps involved in finding the describing function of the above nonlinearity.
- (a) With the help of diagrams define stability and asymptotic stability.
- (b) Explain the Lyapunov's stability theorems. ( $3 \times 20=60$ Marks)