Notes, summaries, assignments, exams, and exercises for Design and Engineering for Baccalaureate

Binding Constraint: LHS equals to RHS at optimal ;  Non-binding constraint: LHS is not equal to RHS at optimal

Shadow Price: Amount by which OFV changes if RHS is increased by one unit

Basic Variable: A decision variable which has non-zero value at optimal ;  Non-basic Value: A decision variable which has a value of zero at optimal

Reduced cost: Amount by which the objective function coefficient needs to be decreased before the variable becomes basic

• Basic var: "Final Value" >0 and "Reduced cost"=0; With allow inc/dec, optimal solution (Final Value) doesn't change, OFV change by (change)*(Final Value); Beyond allow inc/dec, optimal solution and OFV changes by RESOLVE.
• Non basic var:  "Final Value"=0 and "Reduced cost"≠0; In a MIN,"Reduced

Relational Algebra and Relational Calculus

Relational Algebra and Relational Calculus are the formal query languages for a relational model. Both form the base for the SQL language which is used in most of the relational DBMSs. Relational Algebra is a procedural language. On the other hand, Relational Calculus is a declarative language. Relational Algebra and Relational Calculus can be further differentiated on many aspects, which I have discussed below with the help of a comparison chart.

Introduction to Industrial Control Systems

Control systems are fundamental to industrial automation, with a primary focus on Distributed Control Systems (DCS). This document covers the core components, variables, and applications of these systems.

Learning Outcomes

• Describe the components of a control system.
• Define the three types of variables associated with a control system.
• Provide examples of common control systems.
• Explain distributed control systems and their industrial applications.
• List and define components of DCS, including SCADA, communication, and alarms.

Components of an Automation System

A modern automation system is composed of several interconnected components:

• Control System: The brain of the operation, processing inputs and making

Motor Task Analysis and Neuromuscular Mechanisms

Shared Requirements of Motor Tasks

Motor tasks require a highly coordinated neuromuscular effort, adjusting movement to a specific technical model performance. Therefore, all tasks share a high standard of enforcement mechanism.

Four Key Mechanisms of Motor Performance

1. Decision-Memory: The individual selects the motor response based on related past experiences.
2. Neuromuscular Control: The subject performs an automatic check on their muscles.
3. Understanding Implementation (Kinesthetic Feedback): Motion generates impulses originating in sensory organs of a kinesthetic nature. These are perceived by the individual, providing an internal representation of the results.
4. Knowledge of Results (External Feedback)

Translation of Axis

When you need to simplify equations, mainly the conics (circumference, parabola, ellipse, and hyperbola), you need to create a pair of coordinate axes parallel to the originals. This enables working with equations more simply.

This creation of axes is known as parallel translation of axes and consists of moving one or both axes so that the origin moves to a new position, and the axes are parallel to the original.

In the following figure, you can see how you can translate the equations of the curves from one Cartesian plane x and y to a Cartesian plane x’ and y’.

The new origin O’ is defined, and the axes x’ and y’ are parallel to the original axes x and y, so that for a point P(x,y) you have P(x’,y’). With this,...

Robot Kinematics

Euler’s Rotation Theorem

Any rigid body motion that leaves one point fixed can be represented by a single rotation about an axis through the fixed point.

Chasles’ Theorem

Any rigid body motion is the translation of a designated point & a rotation of the whole body about that point.

Kinematic Parameters

These parameters are associated with the kinematic configuration of each link and joint of the robot arm. There are four main kinematic parameters:

Joint Parameters

The relative position and orientation of two successive links can be specified by two joint parameters:

• Joint Angle (θk): The amount of rotation about zk-1 so that Xk-1 is parallel to Xk.
• Joint Distance (dk): The amount of translation along the Zk-1 needed to make

Git Commands and Concepts

Git key commands and concepts:

• add (stage changes)
• commit (with a message)
• head (most recent commit)
• branch (alternative history)
• checkout (enter/exit branch)
• merge (combine into master)
• stash (save without commit, -u for untracked files; latest stashes (0) at the top)
• pop (retrieve a stash)
• fork (copy code from the source into a repository)
• pull (pull remote changes and merge into master)
• revert (undo commits and create a new commit)
• log (history with most recent commits first, -p for patch details)
• rm (--cached to remove from staging)
• fetch (get changes from a remote repository to a local repository without merging them; useful for reviewing changes)
• pull (fetch + merge)
• rebase (create a clean/linear commit history by moving commits

Analog Signal Conversion Process

The analog signal must be captured by a sensor, which converts it into an analog electrical signal. Subsequently, an Analog-to-Digital Converter (ADC) transforms this signal into a sequence of bits.

Advantages and Disadvantages of Digital Signals

Digital signals have a number of advantages over analog:

• They are easier to expand.
• Systems can be applied to reduce the incidence of errors during handling or copying.
• They allow for more varied, simpler, and stacking treatment processes.

Conversely, digitalization requires a greater amount of digital information to achieve quality comparable to the original analog signal. Furthermore, some technical aspects of analog-to-digital conversion and transmission require a high...

Digital Registers

As a flip-flop (FF) can store only one bit of data (a 0 or a 1), it is referred to as a single-bit register. A register is a set of FFs used to store binary data. The storage capacity of a register is the number of bits (1s and 0s) of digital data it can retain.

Loading a Register

Loading a register means setting or resetting the individual FFs—inputting data into the register so that their states correspond to the bits of data to be stored. Loading may be serial or parallel:

• Serial loading: Data is transferred into the register in serial form, i.e., one bit at a time.
• Parallel loading: Data is transferred into the register in parallel form, meaning all the FFs are triggered into their new states at the same time.

Types of Registers

1. Buffer