Obtain a state-space representation of the system shown in Fig.3(a), where uuu is the input and y1y_1y1 and y2y_2y2 are the outputs. Assume that the rollers are frictionless.
Why linearization is necessary? Linearize the nonlinear system z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region 2≤x≤42 \le x \le 42≤x≤4, 10≤y≤1210 \le y \le 1210≤y≤12. Find out the Linearization error at (4, 12).
A closed-loop control system has the characteristics equation s5+3s4+5s3+4s2+s+3=0s^5 + 3s^4 + 5s^3 + 4s^2 + s + 3 = 0s5+3s4+5s3+4s2+s+3=0. Using Routh's stability criterion, determine whether the system is stable or unstable. If unstable how many unstable roots are there?
Simplify the block diagram shown in Fig.2(a). Then obtain the closed loop transfer function C(s)/R(s)C(s)/R(s)C(s)/R(s).
Obtain a state-space representation of the system shown in Fig.2(b).
Why root locus plots are important? Mention the conditions for finding root locus. A negative feedback system has G(s)=k(s+1)(s+2)G(s) = \frac{k}{(s+1)(s+2)}G(s)=(s+1)(s+2)k, H(s)=1H(s)=1H(s)=1. Determine the root loci on the real axis.
Apply Routh's stability criterion on the feedback control system as in Fig. 3(b) and find out the value of kkk for stability.
Linearize the nonlinear system z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region defined by 2≤x≤42 \le x \le 42≤x≤4 and 10≤y≤1210 \le y \le 1210≤y≤12 and find out the linearization error at (4, 12).
Consider the characteristic equations s4+2s3+(4+k)s2+9s+25=0s^4 + 2s^3 + (4+k)s^2 + 9s + 25 = 0s4+2s3+(4+k)s2+9s+25=0 Using Routh's stability criterion, determine the range of K for stability.
Compare between modern control theory and conventional control theory.
Consider the block diagram in Figure 2(c). Simplify the diagram and find out C(s)/R(s)C(s)/R(s)C(s)/R(s).
Consider the negative feedback system having the gain G(s)=k(s+1)(s+2),H(s)=1G(s) = \frac{k}{(s+1)(s+2)}, H(s) = 1G(s)=(s+1)(s+2)k,H(s)=1 For the system Determine the root loci on the real axis. Determine the asymptotes of the root loci. Draw the root loci.
Find out the state-space model for the system shown in Figure 3(b) where uuu is the input and y1y_1y1 and y2y_2y2 are the corresponding output. Assume the rollers are frictionless.
Draw the ladder diagrams to represent AND, OR, NOR, NAND, XOR logic functions respectively.
Draw the functional block diagram of a PLC and explain the PLC architecture.
Why linearization is done? Linearize the nonlinear system z=x2+4xy+6y2z = x^2 + 4xy + 6y^2z=x2+4xy+6y2 in the region defined by 8≤x≤10,2≤y≤48 \le x \le 10, 2 \le y \le 48≤x≤10,2≤y≤4. Find the linearization error at point (10,4)(10, 4)(10,4).
Define the building blocks of a fluid system used to formulate the mathematical modeling.
Derive the relationship between the output, the potential difference across the resistor, and the input for circuit shown in Figure 6(b).
Based on the Figure 6(c), develop equations describing how the temperatures T1T_1T1 and T2T_2T2 will vary with time.
Write down the standard form of state-space equation. Also mention the names of each matrix and vector in the equations. Draw the block diagram of the state-space equations.
For a typical spring-mass-damper system, the characteristic equations can be expressed as follows:
m1y¨1+by˙1+k(y1−y2)=0m_1\ddot{y}_1 + b\dot{y}_1 + k(y_1 - y_2) = 0m1y¨1+by˙1+k(y1−y2)=0 m2y¨2+k(y2−y1)=um_2\ddot{y}_2 + k(y_2 - y_1) = um2y¨2+k(y2−y1)=u
when the output variables are y1y_1y1 and y2y_2y2. Obtain a state-space representation of the system.
What are the basic building blocks for mechanical and electrical systems? Find the analogies between electrical and mechanical system.
What is pneumatic capacitance and pneumatic inertance? Show that pneumatic inertance is inversely proportional to cross-sectional area of a pipe when its length is constant.
Why linearization is necessary? Linearize the nonlinear system z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region defined by 2≤x≤4,10≤y≤122 \le x \le 4, 10 \le y \le 122≤x≤4,10≤y≤12.
Derive the differential equations describing the relationship between the inputs u1u_1u1 and u2u_2u2, the output y1y_1y1 and y2y_2y2 for the system shown in Figure 3(a).
Develop of a mathematical model of the system describing how the output is related to the input. The system is shown in Figure 3(b).
Consider the mechanical system shown in Figure 4(a). Find the state-space model for this single-input, single-output linear system.
Why linearization is important? Linearize the nonlinear equation: z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region defined by 2≤x≤42 \le x \le 42≤x≤4, 10≤y≤1210 \le y \le 1210≤y≤12.
Draw the schematic diagram for control of a double-acting cylinder.