Questions and Answers
What is another name for input in control systems?
Stimulus
What is another name for output in control systems?
Response
Name at least two advantages of a control system.
Power amplification, Remote control
Who is credited for the Root Locus technique?
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Classify the control system based on feedback path.
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List at least three differences between Open and Closed Loop control systems.
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What is another name for input?
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What is another name for output?
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Give at least 2 advantages of control systems.
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Who is credited for the Root Locus Technique?
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Classify control systems based on feedback path.
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Which of the following statements is true regarding open loop control systems?
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Which of the following statements are true regarding closed loop control systems? (Select all that apply)
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What is the ratio of Laplace transform of output to Laplace transform of input called?
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What are the two types of feedback in control systems?
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The natural response describes how the system dissipates or acquires energy.
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Steady state response is the sum of natural and forced responses when the natural response is large.
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What is the transfer function represented by the equation: $\frac{d c(t)}{dt} + 2c(t) = r(t)$?
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What is the transfer function for the system represented by $\frac{d^3 c(t)}{dt^3} + 3\frac{d^2 c(t)}{dt^2} + 5c(t) = 7\frac{d^2 r(t)}{dt^2} + 4\frac{d r(t)}{dt} + 3r(t)$?
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What is the transfer function for the system represented by $\frac{d^2 c(t)}{dt^2} + 6\frac{d c(t)}{dt} + 2c(t) = r(t)$?
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What is the ramp response for a system with the transfer function $G(s) = \frac{s}{(s+4)(s+8)}$?
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What is the ramp response for a system with the transfer function $G(s) = \frac{s}{s^2(s+12)(s+7)}$?
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How is the impedance for a capacitor defined in relation to voltage and current?
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What does Kirchhoff's voltage law state?
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What is the current I1 when 12 volts is applied across a 60 ohm resistor?
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What is the formula used to calculate the voltage drop across a component?
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Study Notes
Course Overview
- ELEN 30123 focuses on Feedback Control Systems at the Polytechnic University of the Philippines, targeting fundamental control theories applied in engineering.
- The grading system encompasses attendance, assignments, quizzes, major exams, and research, contributing to a balanced evaluation.
Course Structure
- Introduction to electrical systems, control systems, and fundamental mathematical methods such as Differential Equations and Laplace Transforms.
- Control System Analysis includes mathematical modeling, time and frequency domain analysis, and system behavior assessment.
- Design and Implementation covers control applications and system design for desired outputs.
Weekly Breakdown
- Week 1: Introduction to course objectives, classroom rules, and instructor profiles.
- Week 2: Basics of control systems, historical context, and role of engineers.
- Week 3: Introduction to modeling in frequency and time domains.
- Week 4: Control system behavior and analysis.
- Week 5: Time response analysis and subsystem integration.
- Week 6: Steady-state error analysis and error specification.
- Week 7: Design techniques for frequency response in control systems.
Instructor Profile
- Benson G. Pulga serves as the instructor with experience in industrial motor controls and electrical equipment maintenance.
- Connections can be made through social media or email for academic inquiries.
Control System Basics
- Control systems are designed to manage the output of processes based on inputs, with different terminologies for input (stimulus) and output (response).
- Applications span multiple domains: biological systems, space exploration, transportation, manufacturing plants, and automation technologies.
Control System Advantages
- Power amplification for enhanced output.
- Remote control capabilities for managing hazardous situations.
- Simplified input formats for user convenience.
- Compensation for disturbances, ensuring accurate operations despite external factors.
System Characteristics
- Transient Response: The system's immediate reaction to input changes.
- Steady State Response: How close the system's output aligns with the desired result over time.
- Stability: System characteristic defined by minimal to no natural responses to inputs.
Classification of Control Systems
- Systems can be classified based on signal types (continuous vs discrete), input/output numbers (SISO vs MIMO), and feedback mechanisms (Open Loop vs Closed Loop).
- Open-Loop Systems: Achieve control without feedback; less accurate and easier to design.
- Closed Loop Systems: Utilize feedback for corrective action; typically more precise but complicated.
Open vs Closed Loop Control Systems
- Open Loop:
- No feedback mechanism.
- Economical but inaccurate.
- Simpler design.
- Closed Loop:
- Feedback path present.
- More expensive but accurate due to continuous monitoring and adjustments.
- Complex to design and implement.
Key Concepts in Control System Analysis
- Assessing transient and steady-state responses is essential for system design and optimization.
- Analyzing current system responses helps in adjusting designs to achieve desired outcomes.
Preparation and Assignments
- Review advanced mathematics, including Differential Equations and Laplace Transforms.
- Familiarize with Circuit Analysis topics to support control system concepts.
- Short quizzes will precede lectures to reinforce learning.### Steady-State Errors and System Analysis
- Steady-state error can be reduced through analysis and corrective actions.
- Achieving stability involves ensuring the natural response approaches zero or exhibits controlled oscillations.
- Total response of a system consists of natural response plus forced response.
Natural vs. Forced Response
- Natural response reflects how a system dissipates or acquires energy, determined by system properties only.
- Forced response relates to external disturbances or errors, influenced by inputs.
- Transient response is primarily governed by natural responses, while steady-state response focuses on the smaller natural responses over time.
Control System Principles
- The design process begins with schematic creation and development of a mathematical model using block diagrams.
- Mathematical modeling often utilizes differential equations transformed by Laplace Transform.
- Block diagrams simplify complex systems into manageable components, depicting interconnections.
Analyzing System Specifications
- Identifying physical systems and their specifications is vital for effective design.
- Evaluate time responses, including transient and steady-state behaviors, to analyze errors and stability.
Types of Feedback in Control Systems
- Positive feedback enhances performance by adding reference input to feedback output.
- Negative feedback also combines reference input and feedback output but functions to stabilize the system.
Transfer Functions
- A transfer function relates the Laplace transform of output to that of the input under zero initial conditions.
- Form is given as T = Output = C(s) and Input = R(s) with adjustments for feedback.
Laplace Transform
- The Laplace Transform converts time-domain functions into the frequency domain, enabling easier manipulation of differential equations.
- It simplifies convolution into multiplication, benefiting various applications in science and engineering.
Partial Fraction Expansion
- This technique breaks down complex functions into simpler components that are easier to transform.
- Conditions include ensuring N(s) is of lesser degree than D(s) for direct expansion.
Application in Electric Networks
- Transfer functions model electric circuits by relating voltage and current under steady-state conditions.
- Components such as resistors, inductors, and capacitors are characterized by specific relationships between voltage and charge.
System Response Problems
- Finding the transfer function involves manipulating differential equations and applying Laplace transforms.
- The system response can be determined through analysis of the differential equation's components and initial conditions involved.
Key Formulae for Derivatives
- Laplace derivatives relationship: For first-order, L{f′(t)} = sL{f(t)} - f(0), and further for second and third-orders by increasing powers of s.
- The integral of a function can be converted through the Laplace Transform to facilitate resolution of complex equations.
Summary Quiz Preparation
- Know alternative terms for input (reference input) and output (controlled variable).
- Understand advantages of control systems, e.g., improving accuracy and stability.
- Root Locus Technique credited to a specific pioneer in control theory.
- Familiarize with distinctions between open-loop and closed-loop systems regarding feedback and accuracy.### Circuit Components
- Capacitor voltage relationship: ( V(s) = C s I(s) )
- Resistor voltage relationship: ( V(s) = R I(s) )
- Inductor voltage relationship: ( V(s) = L s I(s) )
Impedance
- Impedance formula: ( Z(s) = \frac{V(s)}{I(s)} = C s + R + L s )
- For parallel circuits, apply: ( \frac{1}{Z(s)} = \frac{1}{C s} + \frac{1}{R} + \frac{1}{L s} )
- Series circuit involves summation of individual impedances.
Transfer Function Basics
- Conduct analysis by transforming circuit variables to Laplace domain: ( v(t) \to V(s), i(t) \to I(s), vc(t) \to Vc(s) )
- Replace component values using their impedance values.
Steps to Find Transfer Function
- Example query: Find transfer function relating capacitor voltage ( Vc(s) ) to the input voltage ( V(s) ).
- Capacitor voltage derived as: ( Vc(s) = I(s) C s )
- Impedance addends result in higher-order linear equation for circuit behavior: ( V(s) = Vc(s)(s^2LC + sRC + 1) )
Analyzing DC Circuits
- Identify current and voltage signs:
- Current flows from "+" to "-" (lift), indicating a "+" sign.
- Current flows from "-" to "+" (drop), indicating a "-" sign.
- Define the current loop direction, and maintain consistency across loops.
Problem Solving Using Loop Rule
- Apply Ohm’s Law for calculations in circuits:
- ( I = \frac{V}{R} ) and voltage drop calculated as ( V_D = I \times R )
- In any circuit: ( \text{Sum of } I_{\text{in}} = \text{Sum of } I_{\text{out}} )
- Voltage rule states: ( \text{Sum of Voltages in the circuit} = 0 )
Sample Circuit Problem Steps
- Example: To find current ( I1 ):
- Compute ( I1 = \frac{12 \text{ volts}}{60 \text{ ohms}} )
- Results in ( I1 = 0.2 \text{ amps} )
- Voltage drop calculated as: ( V_D = 0.2 \text{ amps} \times 60 \text{ ohms} = 12 \text{ V} )
Additional Circuit Problem Focus
- Tasks may involve identifying multiple currents and voltage drops.
- Consider node voltages across given nodes for comprehensive circuit analysis.
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Description
This quiz introduces students to the fundamentals of feedback control systems as part of ELEN 30123 at the Polytechnic University of the Philippines. Students will learn about basic classroom rules, the grading system, and essential concepts vital for their understanding of the subject matter.
