CONTROL SYSTEM
Lecture-2
The Design Process:
If multiple
Determine Use the blocks, Analyze,
a physical schematic reduce design, and
Draw a Transform to obtain a test
system and the block
functional the physical block diagram, to see that
specification diagram to a
block system into signal-flow requirements
from the diagram,
single block and
diagram. a schematic.
requirements or state-space or specifications
. representation closed-loop are met.
system.
Step 1: Transform Requirements Into a Physical System
Step 2: Draw a Functional Block Diagram
Step 3: Create a Schematic
Step 4: Develop a Mathematical Model (Block Diagram)
Step 5: Reduce the Block Diagram
Step 6: Analyze and Design
1. Find the Laplace transform of f(t)= 𝐴𝑒 −𝑎𝑡 𝑢 𝑡
1
2. Find the inverse Laplace transform of F(s)= .
(𝑠+3)2
3. Given the following differential equation, solve for y(t) if all initial conditions
are zero. Use the Laplace transform.
𝑑2𝑦 𝑑𝑦
+ 12 + 32𝑦 = 32𝑢(𝑡)
𝑑𝑡 2 𝑑𝑡
10
4. Find the inverse Laplace transform of 𝑠(𝑠+2)(𝑠+3)2
PROBLEM: Find the transfer function relating the capacitor voltage, 𝑉𝑐 (𝑠)to the input voltage,
V(s) in Figure 2.3.
Using normal differential equation, using mesh analysis, using node analysis
Problem:For the network of Figure 2.6, find the transfer function,𝑉𝑐 (𝑠)/V(s), using nodal
analysis and a transformed circuit with current sources.
Given the network of Fig, 1(b), find the transfer function
Consider the RLC filter shown in Fig. 1(a) with input voltage Vi(s) and output voltage V0(s) determine
i. The ordinary differential equation describing the system and then derive the transfer function
G(s)=V0(s)/ Vi(s)
ii. For R=0.5Ω, L=0.25 H and C=1F, draw the step response of the system
𝑉𝐿 (𝑠)
Find the transfer function G(s) = for the following network
𝑉(𝑠)
Operational Amplifiers
𝑉 (𝑠)
Find the transfer function,𝑉𝑜(𝑠), for the circuit
𝑖
Translational Mechanical System
Transfer Functions
𝑥2 (𝑠)
Find 𝐹(𝑠)
𝑥2 (𝑠)
Find 𝑈(𝑠)
