## 1. laws of constant acceleration - applied when acceleration is constant, and motion is a straight line

### 1.1. v = u + at

### 1.2. v² = u² + 2as

### 1.3. s = ut + ½at²

## 2. BLOCK DIAGRAM

### 2.1. definition

2.1.1. specialized and high-level flowchart

2.1.2. use very basic geometric shapes

2.1.2.1. boxes

2.1.2.2. circles

### 2.2. how to create/steps

2.2.1. Identify the system

2.2.2. Create and label the diagram

2.2.3. Indicate input and output

2.2.4. Verify accuracy

### 2.3. application(s)

2.3.1. to design new systems

2.3.2. to provide a high-level overview

2.3.2.1. major system components

2.3.2.2. key process participants

2.3.2.3. important working relationships

2.3.3. to describe and improve existing systems

## 3. LAPLACE TRANSFORM

### 3.1. type(s)

3.1.1. Laplace Transform

3.1.2. Inverse Laplace Transform

### 3.2. function(s)

3.2.1. to convert integral and differential equations into algebraic equations

### 3.3. examples

3.3.1. LT of Unit Step Function

3.3.2. Lt of Unit Impulse function

3.3.3. LT of Ramp Function

3.3.4. LT of Exponential Function

### 3.4. properties

3.4.1. linearity

3.4.2. time differentiation

3.4.3. time integration

3.4.4. time shifting – real translation

3.4.5. real convolution

## 4. EQUATION OF MOTIONS

### 4.1. definition

4.1.1. equations that describe the behavior of a physical system

4.1.2. in terms of its motion as a function of time

### 4.2. application(s)

4.2.1. can apply either to particles or bodies of finite size

4.2.2. allow for the direct solution of a dynamics problem, as a function of time

### 4.3. example(s)

## 5. PHYSICAL SYSTEMS

### 5.1. air-conditioning

5.1.1. how it works

5.1.1.1. the cold side of an air conditioner contains the evaporator and a fan that blows air over the chilled coils and into the room

5.1.1.2. the hot side contains the compressor, condenser and another fan to vent hot air coming off the compressed refrigerant to the outdoors

5.1.1.3. in between the two sets of coils, there's an expansion valve. It regulates the amount of compressed liquid refrigerant moving into the evaporator

5.1.1.4. once in the evaporator, the refrigerant experiences a pressure drop, expands and changes back into a gas

5.1.2. function(s)

5.1.2.1. evaporator

5.1.2.1.1. Receives the liquid refrigerant

5.1.2.2. condenser

5.1.2.2.1. Facilitates heat transfer

5.1.2.3. expansion valve

5.1.2.3.1. regulates refrigerant flow into the evaporator

5.1.2.4. compressor

5.1.2.4.1. pump that pressurizes refrigerant

### 5.2. cruise control

5.2.1. how it works

5.2.1.1. uses radar, lidar and vision sensors to sense the presence of vehicles in front of the driver

5.2.1.2. controls the speed of the car to maintain a constant distance between the vehicle in front by application of throttle or brakes

5.2.2. function(s)

5.2.2.1. the system interacts with the driver, allowing the driver to set a desired speed and following distance, and warns the user of impending collisions

## 6. SYSTEM MODELLING

### 6.1. definition

6.1.1. a mathematical representation

6.1.1.1. physical

6.1.1.2. biological

6.1.1.3. information systems

### 6.2. application(s)

6.2.1. differential equation model

6.2.1.1. time domain mathematical model

6.2.1.2. apply basic laws to the given control system

6.2.1.3. get the differential equation in terms of input and output by eliminating the intermediate variable(s)

6.2.2. transfer function model

6.2.2.1. s-domain mathematical model

6.2.2.2. Linear Time Invariant (LTI) system is defined as the ratio of Laplace transform of output

6.2.2.3. Laplace transform of input by assuming all the initial conditions are zero

6.2.3. state space model

6.2.3.1. can be obtained from any one of the two mathematical models

## 7. DIFFERENTIAL EQUATIONS

### 7.1. definition

7.1.1. a mathematical equation that relates some function with its derivatives

### 7.2. function(s)

7.2.1. the functions usually represent physical quantities

7.2.2. the derivatives represent their rates of change

7.2.3. the differential equation defines a relationship between the two

### 7.3. type(s)

7.3.1. Ordinary Differential Equations

7.3.2. Partial Differential Equations

7.3.3. Linear Differential Equations

7.3.4. Non-linear differential equations

7.3.5. Homogeneous Differential Equations

7.3.6. Non-homogenous Differential Equations

## 8. TRANSFER FUNCTIONS

### 8.1. definition

8.1.1. the ratio of the Laplace transform of the output variable to Laplace transform of the input variable (assuming all initial conditions to be zero)

8.1.2. represents the relationship between the output signal of a control system and the input signal, for all possible input values

### 8.2. function(s)

8.2.1. to check

8.2.1.1. the stability of the system

8.2.1.2. time domain and frequency domain characteristics of the system

8.2.1.3. response of the system for any given input

### 8.3. how to obtain

8.3.1. Block Diagram Method

8.3.1.1. transfer function of each element of a control system is represented by a block diagram

8.3.1.2. block diagram reduction techniques are applied to obtain the desired transfer function

8.3.1.3. gives a pictorial representation of a control system

8.3.2. Signal Flow Graphs

8.3.2.1. the modified form of a block diagram is a signal flow graph

8.3.2.2. further shortens the representation of a control system