Feedback and Control Systems
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The document discusses signal flow graph techniques for representing and analyzing feedback control systems. It defines key signal flow graph terminology like nodes, loops, and paths. It also outlines rules for constructing a signal flow graph from a block diagram, including the addition, series connection, and transmission rules. Finally, it introduces Mason's Gain Formula for calculating the overall gain of a system from its signal flow graph representation.
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This document discusses block diagrams and signal flow graphs, which are useful tools for modeling control systems. It begins by explaining what block diagrams are and how they represent the components and signal flows in a system. Signal flow graphs are then introduced as a more compact way to determine the relationships between input and output variables using Mason's gain formula, without needing to reduce the diagram. The document provides examples of block diagram reductions and simple signal flow graphs. It concludes that block diagrams and signal flow graphs provide control engineers a better understanding of systems by describing the connections between components.
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1. A block diagram is a pictorial representation of a system that shows the relationship between inputs and outputs of the entire system.
2. Block diagrams can represent physical systems and use symbols like summing points, gains, and transfer functions.
3. Reduction techniques can be used to simplify block diagrams, such as combining blocks in series or parallel or eliminating feedback loops.
time response analysis
This document provides an analysis of the time response of control systems. It defines time response as the output of a system over time in response to an input that varies over time. The time response analysis is divided into transient response, which decays over time, and steady state response. Different types of input signals are described, including step, ramp, and sinusoidal inputs. Methods for analyzing the first and second order systems are presented, including determining the transient and steady state response. Static error coefficients like position, velocity and acceleration constants are defined for different system types and inputs. Examples are provided to illustrate the analysis of first and second order systems.
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1-3 open loop vs. close loop.
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1. Block diagrams can be used to model both simple and complex systems, and consist of multiple blocks connected to represent the system's functioning.
2. It is often necessary to reduce block diagrams by combining or rearranging blocks for easier analysis and calculation of the transfer function.
3. Common block diagram reduction techniques include combining blocks in cascade or parallel, moving summing or pickoff points, eliminating feedback loops, and swapping summing points.
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This document summarizes key concepts related to signal flow graphs (SFG). It defines the basic elements of an SFG including nodes, branches, input nodes, output nodes, mixed nodes, forward paths, and loops. It explains how to calculate the forward path gain as the product of branch transmittances along a forward path. It also describes Mason's Gain Formula for calculating the transfer function of a system represented by an SFG using determinants based on forward path gains and loop gains. Finally, it outlines the step-by-step process for applying Mason's Gain Formula which involves identifying forward paths and loops, calculating individual and combined loop gains, and determining the numerator and denominator determinants.
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E2MATRIX Research Lab
Opp Phagwara Bus Stand, Backside Axis Bank,
Parmar Complex, Phagwara Punjab (India).
Contact : +91 9041262727
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Simulation tools typically accept full set of Verilog language constructs
Some language constructs and their use in a Verilog description make simulation efficient and are ignored by synthesis tools
Synthesis tools typically accept only a subset of the full Verilog language constructs
In this presentation, Verilog language constructs not supported in Synopsys FPGA Express are in red italics
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Basic design unit
Modules are:
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Similar to Feedback and Control Systems
Block diagram reduction techniques in control systems.ppt
Rule 1 − Check for the blocks connected in series and simplify.
Rule 2 − Check for the blocks connected in parallel and simplify.
Rule 3 − Check for the blocks connected in feedback loop and simplify.
Rule 4 − If there is difficulty with take-off point while simplifying, shift it towards right.
Rule 5 − If there is difficulty with summing point while simplifying, shift it towards left.
Rule 6 − Repeat the above steps till you get the simplified form, i.e., single block.
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This document discusses signal flow graphs and Mason's gain formula for control systems. It begins by defining key terms used in signal flow graphs such as nodes, branches, transmittance, input/output nodes, paths, and loop gains. It then describes properties of signal flow graphs and how Mason's gain formula can be used to determine a system's transfer function from its signal flow graph. The document concludes by providing two example problems that demonstrate how to apply Mason's gain formula to calculate a system's overall transfer function.
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This document provides an overview of a lecture on signal flow graphs and Mason's gain formula in control systems engineering. Key points covered include:
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Electronics & Communication Engineering - Meerut - MIEThttps://www.miet.ac.in › electronics-communication-engg
Since its inception in the year 2001, the ECE departm
Pertemuan 05. SFG (Signal Flow Graph)
The document defines key terms used in signal flow graphs such as input/output nodes, forward/feedback paths, path/loop gains, and non-touching loops. It also provides Mason's rule for determining the transfer function of a system from its signal flow graph representation, which is defined as the ratio of the output to input with adjustments made for any feedback loops that touch the forward paths. Examples are also given of constructing signal flow graphs from block diagrams and applying Mason's rule to solve for various transfer functions.
Signal Flow Graph, SFG and Mason Gain Formula, Example solved with Masson Gai...
Basic Properties of SFG
Definitions of SFG Terms
SFG Algebra
Relation between SFG and block diagram
Mason Gain Formula
Example solved with Masson Gain Formula
CS Mod2AzDOCUMENTS.in.pptx
This document provides information about block diagrams and signal flow graphs. It defines block diagrams as pictorial representations showing the functions of each component and the flow of signals in a system. Blocks represent mathematical operations on input signals to produce outputs. Signal flow graphs also show the flow of signals between nodes in a system and the relationships between signals. The document outlines rules for manipulating block diagrams using block diagram algebra and provides Mason's rule for solving signal flow graphs to determine a system's transfer function based on path and loop gains.
Multiplexer and De multiplexers.docx
IN THIS SLIDE WE HAVE COVERED THE TOPIC OF DIGITAL ELECTRONIS MULTIPLEXER AND DE MULTIPLEXER TOPIC OF COMBINATIONAL CIRCUIT
THANKS FOR READING MY ANIMATION
29-04-2021_CS-II-EEE(A&B)SFG&MASSON'S.pptx
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Ece 415 control systems, fall 2021 computer project 1
This document provides instructions for a control systems computer project. It includes two parts:
Part I has students implement proportional control of a DC motor model in MATLAB. This includes designing open-loop and closed-loop controllers and analyzing step and disturbance responses.
Part II involves further controller design problems, including designing a controller to increase the system type and minimize settling time, analyzing response to a ramp input, and discussing performance limitations.
Computer Organization And Architecture lab manual
The document discusses the implementation of various logic gates and flip-flops. It describes half adders and full adders can be implemented using XOR and AND gates. Binary to gray code and gray to binary code conversions are also explained. Circuit diagrams for 3-8 line decoder, 4x1 and 8x1 multiplexer are provided along with their truth tables. Finally, the working of common flip-flops like SR, JK, D and T are explained through their excitation tables.
Chapter10
This document provides an overview of time-domain analysis and design of control systems. It discusses block diagrams and their simplification through reduction rules. Transient response specifications for control systems are defined, including delay time, rise time, peak time, maximum overshoot, and settling time. The transient response of second-order systems to a unit step input is analyzed. Factors that affect transient response such as damping ratio are explained. Formulas for calculating delay time and rise time of a second-order system based on its damping ratio and natural frequency are also presented.
Csl8 2 f15
The document discusses signal flow graphs (SFG), which provide a graphical representation of the relationship between variables in a system without needing to reduce block diagrams. An SFG consists of nodes and directed branches and can only represent linear systems. The basic elements of an SFG include branches, nodes, paths, loops, and different types of loops. Mason's gain formula is presented for calculating the transfer function of a system from its SFG. Examples are given to demonstrate how to derive an SFG from a block diagram and simultaneous equations, and how to use Mason's formula to solve for paths and loops.
Signal flow graph
This document discusses signal flow graphs and Mason's rule for calculating transfer functions from such graphs. It defines key terms used in signal flow graphs like nodes, branches, paths, loops, and gains. Mason's rule is presented as a way to relate a signal flow graph to the simultaneous equations of the system to determine the overall transfer function T. The formula for T is given as the sum of the products of the forward path gains and the characteristic function Δ over the number of paths. An example is worked through to demonstrate applying Mason's rule.
Block diagram representation 3
The document discusses block diagram representation of systems. It describes that a block diagram shows the relationship between inputs and outputs of a system using blocks. Each block represents a component and is characterized by a transfer function. The document outlines advantages like easy analysis and design, and disadvantages such as not showing energy sources. It also describes drawing block diagrams, closed loop systems, and the block reduction technique to simplify diagrams.
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Feedback and Control Systems
- 1. Feedback and Control Systems SIGNAL FLOW GRAPH
- 2. Signal Flow Graph Technique In the block diagram technique, it involves a number of blocks including feedback blocks which can be complex and can be very confusing. The signal flow graph is another technique used to represent control systems where there are also set of equations *signal flows from one node to another node *the direction of the arrow indicates the flow of single from the input to the output X(s) Y(s)G(s) X Y G (Gain or Transfer Function) (Node for Input) (Node for Output)
- 3. Signal Flow Graph Technique BASIC TERMINOLOGY 1. Node – a point that is used to represent a summing point, take off point or any variable 2. Input Node – the source of outgoing signals 3. Output Node – (aka sink node) the node that receives the incoming signals 4. Mixed Node – the combination of both the input and output node 5. Loop – the closed path that starts from a node and terminates at the same node X1 X2 G1 G2 H X1 X2G1 G2 H Loop Not a Loop
- 4. Signal Flow Graph Technique BASIC TERMINOLOGY 6. Non-touching Loop – if the loops don’t have touching loops between them. 7. Touching Loop – loops with common node/s X1 X2G1 G2 H1 X3G3 G4 H2
- 5. Signal Flow Graph Technique BASIC TERMINOLOGY 8. Forward Path- a path that starts from the input mode and terminates at an output node. It does not cross to any branch or node more than once. X1 X3X2 X4
- 6. Signal Flow Graph Technique RULES: 1. Addition Rule
- 7. Signal Flow Graph Technique RULES: 2. Series Connection 3. Transmission Rule X1 X3X2H1 H2 X1 X3H1H2 X X1 X2 A11 A12 X1 = A11X X2 = A12X
- 8. Procedure for Converting Block Diagram to Signal Flow Graph Step 1: Represent all of the summing points, take-off points, input and output and other variables by nodes. Step 2: Draw an arrow on the branches connecting the nodes and write gain or transmittance or transfer function of block over the arrow. The flow of signals is known by the direction of the arrows. Step 3: Represent all the feedback systems in the same way and also put the sign ( +/-) with the transmittance (or Transfer Function) of each feedback block.
- 9. Procedure for Converting Block Diagram to Signal Flow Graph G1 G2 H1 + - X Input X1 X2 Y Output X X2X1 YG1 G2 -H1 X1= G1X-H1X2 X2=G2X1 Y=X2
- 10. Procedure for Converting Block Diagram to Signal Flow Graph X X2X1 YG1 G2 -H1 X1= G1X-H1X2 X2=G2X1 Y=X2
- 11. Mason’s Gain Formula 𝑇 = ( 𝑘=1 𝑘 𝑃𝑘∆𝑘 ) / ∆ T= The overall transmittance or gain of the system ∆ (𝐺𝑟𝑎𝑝ℎ 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡)= 1- (sum of the gain product of all possible combination of two non-touching loops)-(sum of the gain product of all combination of three non-touching loops)+…. Pk= Gain of the kth forward path ∆𝒌= same as ∆ but formed by loops not touching the kth forward path; 1- (sum of gain of all loops which are not touching the kth forward path)
- 12. Mason’s Gain Formula R(s) C(s)1 G1 G2 G3 G4 G5 1 -H1 -H2-H3
- 13. Mason’s Gain Formula G1 G4 H2 + - R(s) + - + - G2 G3 + H1 C(s)+
- 14. Application of Mason’s Gain Formula to Electrical Network General procedure to solve the electrical network using the Mason’s Gain Formula: 1. Determine the Laplace transform of the given network and redraw in the s-domain. 2. Write down the equations for the different branch currents and node voltages. 3. Simulate each equation by drawing the corresponding signal flow graph. 4. Combine all signal flow graphs to get the total signal flow of the given network. 5. Use Mason’s gain Formula to derive the transfer function of the given network. Example: Find the transfer function of the given electrical network.