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Block diagram

A block diagram is a graphical representation of a system where individual components or functions are depicted as blocks, connected by lines or arrows that indicate the flow of signals, information, or relationships between them.^[1] This visualization simplifies complex systems by abstracting detailed internal workings into high-level modules, making it easier to analyze structure and interactions without delving into specifics like equations or code.^[2] Block diagrams originated in engineering fields such as electrical engineering and control theory during the early 20th century, evolving from early schematic representations to standardized tools for system design and analysis by the mid-1900s.^[3] They gained prominence in control systems to model feedback loops and transfer functions, aiding engineers in predicting system behavior.^[4] In engineering disciplines, block diagrams serve as foundational tools for designing, simulating, and troubleshooting systems, particularly in control theory where they illustrate how inputs are processed through components like amplifiers, filters, and actuators to produce outputs.^[1] For instance, in electrical and mechanical engineering, they represent dynamic systems by showing signal paths and feedback mechanisms, enabling the application of mathematical techniques such as Mason's gain formula for simplification.^[5] Beyond hardware, block diagrams are widely used in software engineering to outline architectural structures, data flows, and module interactions, facilitating modular design and debugging in complex applications.^[6] Key elements of a block diagram include rectangular blocks symbolizing subsystems or operations, directed arrows for input/output signals, summing points for combining signals, and branch points for splitting flows, all of which adhere to standardized notations to ensure clarity and universality across fields.^[4] Variations include functional block diagrams, which emphasize process sequences, and signal flow graphs, which focus on algebraic relationships for quantitative analysis.^[7] These diagrams are integral to tools like MATLAB/Simulink for simulation and to project management practices for workflow modeling, underscoring their versatility in both theoretical and practical contexts.^[1]

Introduction

Definition

A block diagram is a standardized graphical representation of a system, where the system is decomposed into subsystems or components depicted as rectangular blocks, connected by lines or arrows that illustrate interactions, signal flows, or information pathways between them.^[8]^[9] This approach modularizes complex systems into high-level, decoupled units, emphasizing causality and functional dependencies over low-level mechanics.^[10] Key characteristics of block diagrams include their abstraction from physical or technological details, such as specific hardware configurations or circuit values, to prioritize the overall functional relationships and dynamic behavior of the system.^[9] Arrows typically denote the direction of signal propagation or influence, enabling a clear visualization of inputs entering blocks and outputs emerging to connect with subsequent elements.^[10] This abstraction facilitates analysis across diverse domains, including control engineering, electrical systems, and computer science, where it supports modeling of software architectures or hardware interactions.^[8]^[9] In contrast to detailed diagrams like schematics, which specify precise connections, power flows, and component parameters, block diagrams provide a conceptual overview that conceals implementation intricacies to highlight systemic structure and interdependencies.^[11]^[9] This focus on high-level representation makes block diagrams particularly effective for initial system design and understanding without delving into operational minutiae.^[10]

Purpose and Benefits

Block diagrams primarily serve to simplify the representation of complex systems in fields like control engineering, allowing engineers to model interactions between components without immediate recourse to detailed equations or simulations. By visualizing systems as interconnected blocks—each encapsulating a function such as amplification or filtering—they facilitate initial analysis of overall behavior and signal flow. This approach is particularly valuable in preliminary design stages, where rapid iteration on system architecture is essential before committing to implementation.^[12]^[5] A major benefit of block diagrams is their enhancement of understanding system dynamics, as the graphical format reveals cause-and-effect relationships and potential feedback loops that might be obscured in textual or mathematical descriptions. They promote modular thinking by dividing systems into discrete, reusable blocks, which supports scalable design and easier integration of subsystems. Furthermore, these diagrams aid troubleshooting by highlighting points of failure or inefficiency and enable optimization through straightforward reconfiguration of connections to test performance improvements.^[13]^[14] In problem-solving contexts, block diagrams play a crucial role by enabling the decomposition of intricate systems into manageable parts, emphasizing external interfaces and overall functionality while abstracting away internal mechanics. This decomposition allows for targeted analysis of subsystems' contributions to the whole, streamlining the identification of design flaws or enhancements without exhaustive modeling of every element.^[5]^[12]

Historical Development

Origins in Early Engineering

The origins of block diagrams trace back to the early 1920s in electrical engineering, particularly within the context of telephony and radio amplification at Bell Telephone Laboratories, where engineers sought simplified visual representations of complex feedback systems. In 1927, Harold S. Black developed the negative feedback amplifier to stabilize gain and reduce distortion in long-distance telephone lines, employing early block diagram sketches to illustrate the feedback loop structure comprising an amplifier, feedback network, and summing junction.^[15] This approach abstracted detailed circuit schematics into functional blocks connected by signal paths, marking a pivotal shift toward modular system visualization for analysis and design. Black's innovation addressed practical challenges in transatlantic communication, where amplifier instability could degrade signal quality over thousands of miles. By the 1930s, block diagrams evolved from these rudimentary forms into more standardized tools for telephony and nascent control systems, influenced by the need to analyze stability in feedback configurations. Harry Nyquist's 1932 work on regeneration theory at Bell Labs provided the Nyquist stability criterion using frequency-domain contour plots of open-loop transfer functions, laying groundwork for later depictions of closed-loop systems via block diagrams.^[16] This transition from intricate electrical schematics to abstracted blocks facilitated frequency-domain analysis, enabling engineers to predict oscillations and ensure reliable operation in amplifier chains for both radio broadcasting and telephone repeaters. Hendrik Wade Bode advanced stability analysis in the late 1930s through gain-phase margins, with block diagrams integrated in his work on feedback amplifiers during the 1940s, as detailed in his comprehensive 1945 treatise on network analysis.^[17] Key pioneers like Norbert Wiener extended block diagram applications into early cybernetics during World War II, emphasizing feedback in information processing and control. Wiener's 1942 contributions to anti-aircraft fire control at MIT involved stochastic models for predicting target motion, laying groundwork for cybernetic principles outlined in his 1948 book.^[17] Concurrently, the first formal uses of block diagrams appeared in radar systems around 1940 at the MIT Radiation Laboratory, where they represented servomechanisms for antenna tracking and signal processing, simplifying the integration of amplifiers, filters, and feedback loops in high-stakes military applications.^[17] These wartime efforts solidified block diagrams as essential for engineering complex dynamic systems, bridging electrical and control domains.

Evolution in Systems Theory

In the 1940s and 1950s, block diagrams became integral to control theory, particularly through advancements in feedback system analysis led by Hendrik Bode and Rudolf Kalman. Bode's seminal work, Network Analysis and Feedback Amplifier Design (1945), established block diagrams as a standard tool for modeling linear feedback amplifiers and servomechanisms, emphasizing frequency-domain techniques to assess stability and performance.^[18] This integration was accelerated during World War II at the M.I.T. Radiation Laboratory, where engineers like A.C. Hall applied block diagrams to design radar control systems, representing signal flows and transfer functions to mitigate noise and ensure precise tracking.^[17] The Radiation Laboratory Series, particularly Volume 25 Theory of Servomechanisms (1947) by James, Nichols, and Phillips, further standardized block diagram notations and reduction methods for control analysis. By the early 1960s, Rudolf Kalman extended these foundations with his contributions to optimal control and state-space methods, using block diagrams to depict multivariable feedback systems and introduce concepts like controllability and observability, which shifted focus toward time-domain analysis while retaining diagrammatic clarity for complex dynamics.^[19] The 1960s marked a period of standardization for block diagrams in aerospace and computing, driven by practical demands in high-stakes applications. NASA's Apollo program exemplified this adoption, employing block diagrams extensively in simulations and documentation for guidance, navigation, and control systems to model spacecraft trajectories, attitude adjustments, and sensor integrations.^[20] These diagrams facilitated the analysis of hybrid analog-digital feedback loops in the Apollo command and lunar modules, contributing to standardized notations that influenced industry-wide practices in aerospace engineering and early digital computing simulations.^[20] This era's emphasis on modularity and reduction techniques in block representations helped bridge theoretical control models with computational implementations, solidifying their role in multidisciplinary systems design. By the 1980s, block diagrams evolved through digital adaptations in software tools, enabling automated construction and simulation that integrated seamlessly with computer-aided design (CAD) workflows. Early interactive simulators, such as the block diagram editor developed at Carnegie Mellon University, allowed engineers to construct and analyze linear control systems graphically on personal computers, reducing manual computation errors and accelerating iterative design.^[21] This shift was supported by the proliferation of standalone CAD software like AutoCAD (released 1982), which provided vector-based tools for precise diagramming of control architectures, while simulation languages began incorporating block-oriented interfaces to model dynamic behaviors in real-time.^[22] These advancements laid the groundwork for modern CAD integration, where block diagrams transitioned from static sketches to executable models in environments supporting both analysis and hardware implementation.

Core Elements

Blocks and Their Representation

In block diagrams, the primary elements known as blocks serve to encapsulate and represent individual subsystems or components of a larger system, abstracting their dynamic behavior into a simplified graphical form. These blocks are conventionally depicted as rectangular enclosures that contain a label denoting the subsystem's function. In general applications, such as software engineering or process modeling, blocks are labeled descriptively with names like "Database" or "User Interface" to indicate their role. In control systems and signal processing, this often includes a transfer function in the s-domain, such as G(s), which describes the relationship between input and output signals.^[7]^[23]^[24] This representation emphasizes functional characteristics rather than physical implementation details, allowing analysis of overall system performance in a black-box manner. For straightforward operations, such as amplification or integration, a single block is sufficient, labeled simply with a constant gain K or a basic dynamic term like \frac{1}{s} for an integrator in control contexts. In more intricate systems, blocks support hierarchical nesting, where a higher-level block aggregates multiple interconnected sub-blocks to model complex behaviors while maintaining modularity and scalability. This approach facilitates decomposition, enabling detailed analysis of subsystems independently before integration into the full diagram. Rectangular forms predominate in standard applications for clarity and uniformity.^[25]^[23]^[24] Labeling variations enhance the block's utility by specifying interfaces and variables. Input and output ports are typically marked at the block's edges, with arrows indicating signal direction; for instance, an input port might be labeled with a variable, and in control systems, this could be u(t) or U(s) for the input, and y(t) or Y(s) for the output. Internal variables, if relevant for clarity, can be noted within or adjacent to the block, but the emphasis remains on avoiding granular physical attributes like circuit schematics, prioritizing instead the input-output paradigm essential for systems analysis. This convention ensures blocks remain versatile across disciplines.^[23]^[24]^[25]

Connections and Signal Flow

In block diagrams, connections between blocks are established using directed lines or arrows that represent the transfer of signals, such as information, data, or energy, from the output of one block to the input of another.^[7] These arrows follow a standard convention where the direction of the arrowhead explicitly indicates the flow, ensuring a clear visual depiction of how subsystems interact within the overall system.^[24] For instance, branches may split from a single output to multiple destinations, allowing one signal to feed into several subsequent blocks, while in control systems, summing points—often depicted as circles—merge multiple incoming signals into a single output path.^[26] Signal flow notation in block diagrams emphasizes unidirectional paths in forward directions, where signals progress from input to output through sequential blocks without reversal unless specified.^[24] Feedback loops are denoted by arrows that return from later stages back to earlier points, typically to a summing junction in control applications, illustrating how output influences subsequent inputs to achieve system stability or correction.^[26] This notation maintains a logical progression, with all flows aligned to reflect the causal relationships in the modeled process. In non-control contexts, such as software architecture, connections simply indicate data or control flow without specialized junctions. Special elements enhance the representation of signal interactions in specific domains, including junctions that serve as points for addition or subtraction of signals, often depicted as circles with appropriate signs to denote algebraic operations in control diagrams.^[24] Multipliers, shown along connection lines, indicate gains or scaling factors applied to the signal without reference to underlying physical transmission media, focusing solely on the mathematical transformation.^[26] These elements collectively ensure that the diagram accurately conveys the dynamic interconnections essential for system analysis.

Construction Methods

Basic Drawing Principles

Creating a block diagram from a system description requires a structured approach to visually represent the system's components, interactions, and signal flows, ensuring clarity and analytical utility. This process translates abstract system specifications—whether verbal, mathematical, or schematic—into a graphical form that highlights functional relationships without delving into internal details. The goal is to produce a diagram that facilitates understanding, analysis, and communication among engineers. The step-by-step process typically begins with identifying the main components or subsystems, such as actuators, sensors, or processing units, based on the system's functional breakdown. Next, define the inputs and outputs for each component, specifying the signals or variables that enter and exit them to establish boundaries and interfaces. Then, draw rectangular blocks sequentially to represent these components, labeling each with a descriptive name or transfer function to indicate its role. Finally, connect the blocks using directed arrows to depict signal dependencies and flow directions, ensuring arrows point from outputs to inputs of subsequent blocks. This method, derived from standard modeling practices in feedback systems, allows for iterative refinement as the system's dynamics become clearer. Layout best practices emphasize readability and logical progression to avoid clutter and misinterpretation. Arrange blocks in a left-to-right or top-to-bottom orientation to mimic the natural flow of information or time in the system, which aligns with conventional engineering visualization. Group related components, such as those in parallel paths or feedback loops, into clusters to highlight subsystems and reduce visual complexity. Maintain consistency in block shapes (typically rectangles), line styles for connections (straight lines with arrows), and spacing to ensure the diagram remains scalable and interpretable at a glance. Block diagrams can be produced using various tools and media, ranging from simple hand-drawn sketches on paper for preliminary ideation to sophisticated digital software for precise and editable representations. Microsoft Visio offers templates and stencils tailored for engineering diagrams, enabling easy drag-and-drop construction and export options. For control systems specifically, MATLAB with its Simulink toolbox provides an integrated environment to draw, simulate, and analyze block diagrams, supporting dynamic updates and computational validation. These tools enhance accuracy and collaboration while preserving the diagram's role as a foundational engineering artifact.

Notation Standards

Block diagrams employ standardized symbols to ensure clarity and uniformity in representing system components across engineering disciplines. Rectangles are conventionally used to depict processes or functional blocks, encapsulating the transformation from input to output signals, such as a transfer function G(s).^[27] Circles represent summing points, where multiple input signals are algebraically combined, often marked with a '+' for addition or '-' for subtraction to indicate the operation.^[27] Arrows denote the direction of signal flow, typically labeled with variables like input r(t) or output c(t), facilitating the tracing of information paths.^[27] Discipline-specific adaptations refine these symbols for particular fields. In electronics and electrical engineering, the IEEE Std 315-1975 outlines graphic symbols for diagrams, including rectangular blocks for functional units and standardized symbols such as triangles for amplifiers, along with standardized arrowheads and connection lines to maintain consistency in schematic representations.^[28] For general systems engineering, the ISO 14617-1 standard establishes rules for graphical symbols in diagrams, promoting rectangles for basic elements, circular nodes for junctions, and directed lines for flows, applicable to process and control contexts internationally.^[29] Common conventions enhance readability and analytical utility. Blocks are often numbered sequentially (e.g., Block 1, Block 2) for identification, enabling precise referencing during reduction or simulation processes.^[30]

Types and Variations

Functional Block Diagrams

Functional block diagrams represent the functional architecture of a system by illustrating the flow of inputs through processing elements to produce outputs, focusing on operational relationships rather than detailed implementation or mathematical models. These diagrams are commonly used in systems and control engineering, with applications in mechanical and process engineering to conceptualize system behaviors, such as material or energy transformations, enabling engineers to identify key interactions early in the design phase.^[31]^[32]^[33] A primary feature of functional block diagrams is their depiction of sequential operations, typically arranged from left to right to indicate the temporal or logical progression of functions, with arrows denoting the direction of flow for signals, materials, or data. Rectangular blocks symbolize individual functions, such as transformation or decision points, while feedback loops are integrated to model control aspects, where outputs influence subsequent inputs to maintain system stability or adjust processes dynamically. This structure supports modular analysis, allowing subsystems to be isolated and examined independently.^[31]^[8]^[34] In mechanical engineering, functional block diagrams often illustrate manufacturing processes, for instance, outlining the sequence from raw material input through cutting, forming, and assembly blocks to finished product output, with feedback from quality inspection to rework earlier stages if defects are detected. In process engineering contexts, a distillation process can be represented with blocks for feed input, separation, and product streams, highlighting material and energy flows without specifying detailed equipment.^[35]

Reduction and Analysis Diagrams

Reduction and analysis diagrams represent block diagrams specifically tailored for mathematical simplification of complex systems to obtain overall transfer functions. These diagrams facilitate the derivation of a system's input-output relationship, expressed as a transfer function H(s), by reducing interconnected blocks through algebraic manipulations. This process is essential in control systems engineering for analyzing stability and performance without simulating the entire system.^[24] The primary purpose of these diagrams is to simplify representations of dynamic systems, where each block denotes a transfer function, and connections indicate signal flows. By applying reduction rules, engineers derive the equivalent single-block transfer function, such as H(s) = G_1(s) \cdot G_2(s) for blocks in series, highlighting how individual component behaviors combine multiplicatively. This reduction enables analytical evaluation of system responses in the Laplace domain.^[24] Key techniques include series and parallel reductions, as well as manipulations involving summing points and feedback loops. In series configurations, the overall gain is the product of individual block gains, H(s) = \prod G_i(s), assuming no branching. Parallel blocks combine additively, yielding H(s) = \sum G_i(s), based on superposition at the summing junction. Blocks can be moved across summing points by scaling inputs or outputs accordingly; for instance, shifting a block backward past a summing point applies its gain to all incoming signals. Feedback reductions transform closed loops into equivalent forward paths, such as H(s) = \frac{G(s)}{1 + G(s)H(s)} for unity negative feedback. These rules iteratively simplify diagrams until a single transfer function emerges.^[24] For more intricate interconnections, Mason's gain formula serves as a powerful tool, converting block diagrams to signal-flow graphs for direct computation of the transfer function without stepwise reduction. Developed by Samuel J. Mason, the formula calculates the overall gain as T(s) = \sum_k P_k \Delta_k / \Delta, where P_k are forward path gains, \Delta is the graph determinant accounting for loop interactions, and \Delta_k excludes loops touching the k-th path. This method efficiently handles multiple loops and paths, providing the equivalent H(s) for analysis.^[36]^[37] Other variations include block flow diagrams, particularly in process engineering for depicting major material and energy streams between unit operations, and signal flow graphs, which emphasize algebraic paths for quantitative analysis in control theory.^[33]

Applications

In Control Systems Engineering

In control systems engineering, block diagrams serve as a fundamental tool for modeling and analyzing feedback loops, enabling engineers to visualize the dynamic interactions between system components. They depict the flow of signals from reference inputs through controllers, plants, and sensors back to the feedback path, facilitating the design of systems that maintain desired outputs despite variations or perturbations. This representation is essential for understanding how control actions influence system behavior in applications such as process regulation and motion control.^[5] A typical closed-loop block diagram illustrates the plant as the core process being controlled, the controller as the mechanism generating corrective signals, and sensors as devices measuring the output for feedback. For instance, in a speed control system, the plant might represent a motor's dynamics, the controller adjusts input voltage based on error signals, and the sensor (e.g., a tachometer) provides velocity feedback to close the loop. This structure allows engineers to identify key elements like summing junctions for error computation and actuators for input application, ensuring the diagram captures the causal relationships in the system./04%3A_Control_System_Design_Objectives/4.04%3A_Disturbance_Rejection) Specific concepts such as forward path gains and disturbance inputs are integral to these diagrams. The forward path gain quantifies the overall amplification from the error signal to the plant output, often denoted as the product of transfer functions along the path, which determines the system's responsiveness. Disturbance inputs, modeled as external signals entering at various points (e.g., load changes affecting the plant), are incorporated to assess how the feedback loop rejects unwanted effects, with paths shown branching into the main flow. Stability analysis relies on block manipulation to simplify these diagrams, revealing characteristics like gain margins through equivalent transfer functions.^[38]/04%3A_Control_System_Design_Objectives/4.04%3A_Disturbance_Rejection).pdf) Historically, block diagrams became prominent in control systems engineering during the mid-20th century, particularly in the design of proportional-integral-derivative (PID) controllers following the Ziegler-Nichols tuning method introduced in 1942 and widely adopted in industrial applications by the 1950s. This era saw their integration into servomechanism designs at institutions like MIT's Servomechanisms Laboratory, where they aided in simulating and refining feedback systems for wartime and postwar technologies.^[39]^[40]

In Signal Processing and Electronics

In signal processing and electronics, block diagrams provide a high-level representation of signal paths by depicting components such as filters, amplifiers, and modulators as cascaded blocks, allowing engineers to visualize linear transformations without delving into detailed circuit schematics. This approach facilitates the analysis of how input signals propagate through the system, with each block encapsulating a specific operation like amplification or frequency filtering. For instance, an amplifier block might multiply the input signal by a gain factor, while a filter block applies a transfer function to shape the frequency content.^[41]^[42] Key features of these diagrams include the explicit modeling of frequency responses, where blocks represent operations that alter the signal's spectrum—such as low-pass filters attenuating high frequencies—and the tracing of noise paths to assess signal integrity in noisy environments. Unlike detailed transistor-level schematics, block diagrams abstract these elements to focus on overall system behavior, enabling quick identification of bottlenecks like noise injection in amplification stages. This abstraction is particularly valuable in digital signal processing implementations, where blocks correspond to algorithmic units executed on hardware like DSP chips or FPGAs.^[41]^[42] Representative examples illustrate their utility: in audio processing chains, block diagrams outline sequences from analog-to-digital conversion through equalization filters and digital amplifiers to output, as seen in perceptual audio coding systems where blocks handle psychoacoustic modeling and bit allocation for compression. Similarly, in RF systems, they map signal flows from low-noise amplifiers and mixers to digital downconverters, aiding the design of software-defined radios where modulation blocks process carrier signals for wireless transmission. These diagrams, often akin to functional block representations, streamline prototyping and simulation in tools like MATLAB Simulink.

Advantages and Limitations

Key Advantages

Block diagrams offer visual clarity in representing complex system interactions, allowing engineers to depict components, signals, and feedback loops in a straightforward graphical format that reveals operational insights not easily discernible from textual descriptions. This graphical approach highlights the flow of signals and relationships between subsystems, making it easier to identify key dynamics such as input-output paths and potential bottlenecks.^[30]^[43] Their ease of modification further enhances utility in iterative design processes, as blocks and connections can be rearranged or simplified using established equivalences without altering the underlying mathematical representation, thereby streamlining analysis and adjustments during system development. This flexibility supports rapid prototyping and refinement, particularly in control systems where feedback structures must be tested and optimized. Scalability is another core strength, enabling representation from simple single-loop configurations to hierarchical models of large-scale systems, where techniques like Mason's gain formula facilitate handling increased complexity.^[30] Block diagrams also promote interdisciplinary utility by serving as a bridge between technical experts and non-technical stakeholders, providing an intuitive visual language that conveys system architecture and functionality without requiring deep mathematical knowledge. This accessibility fosters better collaboration in multidisciplinary teams, such as those involving engineers, managers, and clients, by translating abstract concepts into relatable diagrams that support decision-making across domains. Engineering studies highlight that such visual tools can accelerate initial modeling phases, often reducing design iteration time through clearer communication and fewer misunderstandings.^[6]^[30]

Common Limitations

Block diagrams, while effective for high-level system representation, often oversimplify complex dynamics by abstracting away nonlinear behaviors and precise timing dependencies, assuming linearity and time-invariance that may not hold in real-world systems.^[44] This abstraction prevents reliance on superposition principles, as the order of nonlinear elements cannot be rearranged without altering system response, leading to incomplete models of phenomena like saturation or hysteresis.^[44] In scenarios involving complex feedback loops, block diagrams introduce ambiguity in path identification and signal flow, particularly with multiple nested or interdependent loops, making manual tracing error-prone and inefficient compared to symbolic algebraic methods.^[45]^[46] Such representations lack a formal grammar for systematic manipulation, complicating redesign or verification in intricate configurations.^[45] Block diagrams are inherently graphical and qualitative, necessitating supplementary mathematical formulations—such as transfer functions or state-space equations—for quantitative precision and rigorous analysis, as the diagrams alone cannot resolve stability or performance metrics accurately.^[45] They prove inadequate for very detailed implementations, where atomic- or component-level specifics are required, as the high-level abstraction becomes cluttered and obscures implementation nuances like circuit topology or parameter variations. Similarly, block diagrams are not suitable for nanoscale or quantum systems demanding atomic-level detail, where classical signal-flow assumptions fail to account for quantum effects such as coherence and entanglement, requiring instead quantum-specific models like Hamiltonians or density matrices.^[47]

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[45]
[PDF] 3 Block diagrams and operators: Two new representations
Block diagrams visually represent a system. To show how they work ... Here is the difference equation for the simplest feedback system, an accu mulator:.Missing: history control
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[PDF] INTERCONNECTED SYSTEMS AND FEEDBACK ).
Note that the plus sign in the denominator is a result of choosing the minus sign on the lower (feedback) input to the adder in the block diagram of Figure 5.2- ...
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[PDF] Rules for Reduced Complexity Block Diagrams
If rendered in full detail, top level block diagrams rapidly become cluttered, unmanageable, and cease to provide useful information to the reader. This format ...
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Principles and applications of quantum control engineering - Journals
Nov 28, 2012 · It is convenient to use block diagram techniques in classical control ... limitations of vacuum tube valves. Time will of course tell, but ...