*Control System Block Manipulation RoyMech Chapter 4. Simple Control Systems. Slope of road Desired velocity Throttle. F Velocity Controller. Engine Body в€’ ОЈ ОЈ. Figure 4.2. Block diagram of a car with cruise control.*

Basics of State Space Modeling Department of Electrical. Concept Building Through Block Diagram Using Matlab/Simulink. Uploaded by. M. Gulzar Manual Solution We will solve an example of block diagram to find its canonical form. The step by step solution is given below in fig 5 Fig. 4 Basic Block Diagram Transformations III. Advantages and Disadvantages Of Block Diagrams Block diagram representation of any system offers the following вЂ¦, Block diagram reduction rules help you to minimize the block diagram thus solving the equations quickly. Below table represents block diagram reduction rules in the control system . Using the above rules you have to follow below simple steps to solve the block diagrams: 1. Combine all cascade blocks 2. Combine all parallel blocks 3. Eliminate all minor (interior) feedback loops 4. Shift.

NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 2 Information Organization through Block Diagram Chapter 4. Simple Control Systems. Slope of road Desired velocity Throttle. F Velocity Controller. Engine Body в€’ ОЈ ОЈ. Figure 4.2. Block diagram of a car with cruise control.

Control Systems Questions and Answers вЂ“ Block diagram Algebra Posted on May 21, 2017 by Manish This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on вЂњBlock diagram вЂ¦ 2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦

Problems Of Block Diagram Reduction In Control System please fill out registration form to access in our databases. Summary : Note the transfer function present in this single block is the transfer function of the overall block diagram example consider the block diagram shown in the following figure let us simplify reduce this block diagram using the block diagram reduction rules step 1 use ANALYSIS AND SIMULATION OF CONTROL SYSTEMS USING MATLAB MATLAB can be used to analyze systems described by transfer functions or state space. Since transfer functions are ratio of polynomials, let us see how MATLAB handles polynomials. POLYNOMIALS Polynomials in MATLAB are represented by a vector containing the coefficients in descending order. For example, the roots вЂ¦

Click on download link below to download the 'control-system-block-diagram-reduction-problems-pdf' PDF for free problems solve for x y and or in each diagram PDF results The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative

Block Diagram in control systems. Any system can be described by a set of differential equations, or it can be represented by the schematic diagram that contains all the components and their connections. An example controlling a mechanical system is taken and the unexpected outside element effect consider here as disturbance, the close-loop feedback transfer function of the system.

An example controlling a mechanical system is taken and the unexpected outside element effect consider here as disturbance, the close-loop feedback transfer function of the system. Figure 8.1 shows a block diagram for a typical control system, consisting of a process to be controlled and a (dynamic) compensator, connected in a feed- back loop.

example, from this DT system block diagram the difference equation can be determined. yn [] =2xn []!xn!1 [ ]! 1 2 yn!1 [ ] 7/21/06 M.J.Roberts-AlRightsReserved.EditedbyDr.RobertAkl 3 Block Diagrams and Transfer Functions From a z-domain block diagram the transfer function can be determined. Yz =2Xz ()!z!1Xz ()! 1 2 z!1Yz Hz = Yz Xz = 2!z!1 1+ 1 2 z!1 = 2z!1 z+ 1 2 7/21/06 M.J.Roberts Block diagram reduction rules help you to minimize the block diagram thus solving the equations quickly. Below table represents block diagram reduction rules in the control system . Using the above rules you have to follow below simple steps to solve the block diagrams: 1. Combine all cascade blocks 2. Combine all parallel blocks 3. Eliminate all minor (interior) feedback loops 4. Shift

ANALYSIS AND SIMULATION OF CONTROL SYSTEMS USING MATLAB MATLAB can be used to analyze systems described by transfer functions or state space. Since transfer functions are ratio of polynomials, let us see how MATLAB handles polynomials. POLYNOMIALS Polynomials in MATLAB are represented by a vector containing the coefficients in descending order. For example, the roots вЂ¦ Kamman вЂ“ Control Systems вЂ“ Block Diagram Examples вЂ“ page: 1/8 ME 3600 Control Systems Block Diagram Reduction Examples Example 1: R.C. Dorf and R.H. Bishop, Modern Control Systems, 11th Ed., Pearson Prentice-Hall, 2008.

discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams. An example controlling a mechanical system is taken and the unexpected outside element effect consider here as disturbance, the close-loop feedback transfer function of the system.

Block Diagram Reduction Signal-Flow Graphs Unit 4: Block Diagram Reduction Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Figure 8.1 shows a block diagram for a typical control system, consisting of a process to be controlled and a (dynamic) compensator, connected in a feed- back loop.

Control System Block Manipulation RoyMech. A reliability block diagram (RBD) is a drawing and calculation tool used to model complex systems. An RBD is a series of images (blocks) representing portions of a system. Once the images (blocks), Figure 8.1 shows a block diagram for a typical control system, consisting of a process to be controlled and a (dynamic) compensator, connected in a feed- back loop..

Control Systems/Signal Flow Diagrams Wikibooks open. 2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦, Kamman вЂ“ Control Systems вЂ“ Block Diagram Examples вЂ“ page: 1/8 ME 3600 Control Systems Block Diagram Reduction Examples Example 1: R.C. Dorf and R.H. Bishop, Modern Control Systems, 11th Ed., Pearson Prentice-Hall, 2008..

To Perform a Block Diagram Reduction Using MATLAB _ Matlab. 2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦ https://en.wikipedia.org/wiki/Signal-flow_graph System Dynamics and Control Block Diagrams Dr Stefan Williams Dr. Stefan B. Williams Amme 3500 : Introduction Slide 2 Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling.

3 Block diagrams and operators: Two new representations. 35. Exercise 12. Although this section pointed out a disadvantage of difference equations, it is also important to appreciВ ME 413 Systems Dynamics & Control Chapter 10: Time-Domain Analysis and Design of Control Systems 9/11 Example 5 Use block diagram algebra to solve the previous example.

The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative creasing complexity gives students conп¬Ѓdence in their problem-solving ability as they work their way from the exercises to the design and computer-based problems. It is assumed that instructors (and students) have access to MATLAB and the Control System Toolbox or to LabVIEW and the MathScript RT Module. All of the computer solutions in this SolutionManualwere devel-oped and tested on an

In Fig. 6, (a) shows the block diagram of an example dynamic system and figures (b) to (f) show the successive reductions of the block diagram. The rules that need to be applied for each successive reduction in the current practice and by using the proposed alternative approach are summarized in Table 1. As a second example, we simplify the multipleloop system as shown in Fig. 7 [Figs 3В±9 in Figure 2 is an example of a block diagram showing a simple closed-loop control system. The diagram details a controller, and shows a plant with no detail. In the controller the command, The diagram details a controller, and shows a plant with no detail.

Block Diagram Reduction Signal-Flow Graphs Unit 4: Block Diagram Reduction Engineering 5821: Control Systems I Faculty of Engineering & Applied Science ME 413 Systems Dynamics & Control Chapter 10: Time-Domain Analysis and Design of Control Systems 9/11 Example 5 Use block diagram algebra to solve the previous example.

An example controlling a mechanical system is taken and the unexpected outside element effect consider here as disturbance, the close-loop feedback transfer function of the system. 2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦

discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams. 5/10/2014В В· Example 5.1: Reduce the block diagram shown in Figure 5.9 to a single transfer function. FIGURE 5.9 Block diagram for Example 5.1. Solution: We solve the вЂ¦

Home Control Index. Control System Block Manipulation. The table below relates the control block symbols to the control equation and also illustrates how changes in the control block arrangements can be changed whilst retaining the original control function. Block Diagram Reduction Signal-Flow Graphs Unit 4: Block Diagram Reduction Engineering 5821: Control Systems I Faculty of Engineering & Applied Science

Block Diagram Reduction W.3 4Masonв„ўs Rule and the Signal-Flow Graph A compact alternative notation to the block diagram is given by the signal-вЃ„ow graph introduced Signal-вЃ„ow by S. J. Mason (1953, 1956). As with the block diagram, the signal-вЃ„ow graph oвЃ„ers a visual tool for graph representing the causal relationships between the components of the system. The method consists of 5/10/2014В В· Example 5.1: Reduce the block diagram shown in Figure 5.9 to a single transfer function. FIGURE 5.9 Block diagram for Example 5.1. Solution: We solve the вЂ¦

Block Diagram Reduction W.3 4Masonв„ўs Rule and the Signal-Flow Graph A compact alternative notation to the block diagram is given by the signal-вЃ„ow graph introduced Signal-вЃ„ow by S. J. Mason (1953, 1956). As with the block diagram, the signal-вЃ„ow graph oвЃ„ers a visual tool for graph representing the causal relationships between the components of the system. The method consists of A reliability block diagram (RBD) is a drawing and calculation tool used to model complex systems. An RBD is a series of images (blocks) representing portions of a system. Once the images (blocks)

Figure 2 is an example of a block diagram showing a simple closed-loop control system. The diagram details a controller, and shows a plant with no detail. In the controller the command, The diagram details a controller, and shows a plant with no detail. Problems Of Block Diagram Reduction In Control System please fill out registration form to access in our databases. Summary : Note the transfer function present in this single block is the transfer function of the overall block diagram example consider the block diagram shown in the following figure let us simplify reduce this block diagram using the block diagram reduction rules step 1 use

Basics of State Space Modeling Department of Electrical. Kamman вЂ“ Control Systems вЂ“ Block Diagram Examples вЂ“ page: 1/8 ME 3600 Control Systems Block Diagram Reduction Examples Example 1: R.C. Dorf and R.H. Bishop, Modern Control Systems, 11th Ed., Pearson Prentice-Hall, 2008., Home Control Index. Control System Block Manipulation. The table below relates the control block symbols to the control equation and also illustrates how changes in the control block arrangements can be changed whilst retaining the original control function..

Control System Block Diagram javatpoint. example, from this DT system block diagram the difference equation can be determined. yn [] =2xn []!xn!1 [ ]! 1 2 yn!1 [ ] 7/21/06 M.J.Roberts-AlRightsReserved.EditedbyDr.RobertAkl 3 Block Diagrams and Transfer Functions From a z-domain block diagram the transfer function can be determined. Yz =2Xz ()!z!1Xz ()! 1 2 z!1Yz Hz = Yz Xz = 2!z!1 1+ 1 2 z!1 = 2z!1 z+ 1 2 7/21/06 M.J.Roberts, An example controlling a mechanical system is taken and the unexpected outside element effect consider here as disturbance, the close-loop feedback transfer function of the system..

NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 2 Information Organization through Block Diagram Problems Of Block Diagram Reduction In Control System please fill out registration form to access in our databases. Summary : Note the transfer function present in this single block is the transfer function of the overall block diagram example consider the block diagram shown in the following figure let us simplify reduce this block diagram using the block diagram reduction rules step 1 use

NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 2 Information Organization through Block Diagram discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams.

Control Systems Questions and Answers вЂ“ Block diagram Algebra Posted on May 21, 2017 by Manish This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on вЂњBlock diagram вЂ¦ 2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦

The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative Block Diagram Reduction Signal-Flow Graphs Unit 4: Block Diagram Reduction Engineering 5821: Control Systems I Faculty of Engineering & Applied Science

ANALYSIS AND SIMULATION OF CONTROL SYSTEMS USING MATLAB MATLAB can be used to analyze systems described by transfer functions or state space. Since transfer functions are ratio of polynomials, let us see how MATLAB handles polynomials. POLYNOMIALS Polynomials in MATLAB are represented by a vector containing the coefficients in descending order. For example, the roots вЂ¦ Click on download link below to download the 'control-system-block-diagram-reduction-problems-pdf' PDF for free problems solve for x y and or in each diagram PDF results

Dr.Laith Abdullah Mohammed Homework: Draw the block diagram of the control system for the following cases: 1. Computer Disk Drive. 2. Video Game. 3. Block Diagram Reduction Three primary situations for reducing block diagrams to simpler forms: Example #3 - Step #1 U(s) + - - a s 1 2 s 1 a 1 a 0 Y(s) + b 0 + b 1 Re-draw slightly, then close this feedback loop + Example #3 - Step #2a U(s) + - 2 1 a s a 1 + s 1 a 0 Y(s) + b 0 + b 1 Cannot have a вЂњpick-offвЂќ in middle of feedback loop! Cannot have a вЂњpick-offвЂќ in in middle of

Block Diagram Reduction Signal-Flow Graphs Unit 4: Block Diagram Reduction Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Block Diagram Reduction Three primary situations for reducing block diagrams to simpler forms: Example #3 - Step #1 U(s) + - - a s 1 2 s 1 a 1 a 0 Y(s) + b 0 + b 1 Re-draw slightly, then close this feedback loop + Example #3 - Step #2a U(s) + - 2 1 a s a 1 + s 1 a 0 Y(s) + b 0 + b 1 Cannot have a вЂњpick-offвЂќ in middle of feedback loop! Cannot have a вЂњpick-offвЂќ in in middle of

cepts, such as control instrumentation diagrams and control block diagrams, are intro- duced in the next examples, it is important that you study them thoroughly. Example 1.1: Surge Tank Concept Building Through Block Diagram Using Matlab/Simulink. Uploaded by. M. Gulzar Manual Solution We will solve an example of block diagram to find its canonical form. The step by step solution is given below in fig 5 Fig. 4 Basic Block Diagram Transformations III. Advantages and Disadvantages Of Block Diagrams Block diagram representation of any system offers the following вЂ¦

In Fig. 6, (a) shows the block diagram of an example dynamic system and figures (b) to (f) show the successive reductions of the block diagram. The rules that need to be applied for each successive reduction in the current practice and by using the proposed alternative approach are summarized in Table 1. As a second example, we simplify the multipleloop system as shown in Fig. 7 [Figs 3В±9 in System Dynamics and Control Block Diagrams Dr Stefan Williams Dr. Stefan B. Williams Amme 3500 : Introduction Slide 2 Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling

3 Block diagrams and operators: Two new representations. 35. Exercise 12. Although this section pointed out a disadvantage of difference equations, it is also important to appreciВ Chapter 4. Simple Control Systems. Slope of road Desired velocity Throttle. F Velocity Controller. Engine Body в€’ ОЈ ОЈ. Figure 4.2. Block diagram of a car with cruise control.

Control System Block Diagram javatpoint. Figure 2 is an example of a block diagram showing a simple closed-loop control system. The diagram details a controller, and shows a plant with no detail. In the controller the command, The diagram details a controller, and shows a plant with no detail., example, from this DT system block diagram the difference equation can be determined. yn [] =2xn []!xn!1 [ ]! 1 2 yn!1 [ ] 7/21/06 M.J.Roberts-AlRightsReserved.EditedbyDr.RobertAkl 3 Block Diagrams and Transfer Functions From a z-domain block diagram the transfer function can be determined. Yz =2Xz ()!z!1Xz ()! 1 2 z!1Yz Hz = Yz Xz = 2!z!1 1+ 1 2 z!1 = 2z!1 z+ 1 2 7/21/06 M.J.Roberts.

Control System Block Manipulation RoyMech. example, from this DT system block diagram the difference equation can be determined. yn [] =2xn []!xn!1 [ ]! 1 2 yn!1 [ ] 7/21/06 M.J.Roberts-AlRightsReserved.EditedbyDr.RobertAkl 3 Block Diagrams and Transfer Functions From a z-domain block diagram the transfer function can be determined. Yz =2Xz ()!z!1Xz ()! 1 2 z!1Yz Hz = Yz Xz = 2!z!1 1+ 1 2 z!1 = 2z!1 z+ 1 2 7/21/06 M.J.Roberts, The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative.

To Perform a Block Diagram Reduction Using MATLAB _ Matlab. discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams., Figure 2 is an example of a block diagram showing a simple closed-loop control system. The diagram details a controller, and shows a plant with no detail. In the controller the command, The diagram details a controller, and shows a plant with no detail..

Control System Block Diagram javatpoint. cepts, such as control instrumentation diagrams and control block diagrams, are intro- duced in the next examples, it is important that you study them thoroughly. Example 1.1: Surge Tank https://en.wikipedia.org/wiki/Control_(science) Block diagram reduction rules help you to minimize the block diagram thus solving the equations quickly. Below table represents block diagram reduction rules in the control system . Using the above rules you have to follow below simple steps to solve the block diagrams: 1. Combine all cascade blocks 2. Combine all parallel blocks 3. Eliminate all minor (interior) feedback loops 4. Shift.

discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams. Examples of blocks that do not execute include Terminator blocks, disabled Assertion blocks, S-Function blocks configured for block reduction, and To Workspace blocks when MAT-file logging is disabled for code generation.

5/10/2014В В· Example 5.1: Reduce the block diagram shown in Figure 5.9 to a single transfer function. FIGURE 5.9 Block diagram for Example 5.1. Solution: We solve the вЂ¦ Concept Building Through Block Diagram Using Matlab/Simulink. Uploaded by. M. Gulzar Manual Solution We will solve an example of block diagram to find its canonical form. The step by step solution is given below in fig 5 Fig. 4 Basic Block Diagram Transformations III. Advantages and Disadvantages Of Block Diagrams Block diagram representation of any system offers the following вЂ¦

Block Diagram in control systems. Any system can be described by a set of differential equations, or it can be represented by the schematic diagram that contains all the components and their connections. The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative

2 Examples. 2.1 Solving a signal-flow graph by systematic reduction : (just like in block diagrams). Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system. An example of a signal flow diagram. Forward Paths . A forward path is a path in the signal flow diagram that connects вЂ¦ Block diagram reduction rules help you to minimize the block diagram thus solving the equations quickly. Below table represents block diagram reduction rules in the control system . Using the above rules you have to follow below simple steps to solve the block diagrams: 1. Combine all cascade blocks 2. Combine all parallel blocks 3. Eliminate all minor (interior) feedback loops 4. Shift

Home Control Index. Control System Block Manipulation. The table below relates the control block symbols to the control equation and also illustrates how changes in the control block arrangements can be changed whilst retaining the original control function. ME 413 Systems Dynamics & Control Chapter 10: Time-Domain Analysis and Design of Control Systems 9/11 Example 5 Use block diagram algebra to solve the previous example.

Block Diagram in control systems. Any system can be described by a set of differential equations, or it can be represented by the schematic diagram that contains all the components and their connections. Figure 8.1 shows a block diagram for a typical control system, consisting of a process to be controlled and a (dynamic) compensator, connected in a feed- back loop.

Block diagram reduction rules help you to minimize the block diagram thus solving the equations quickly. Below table represents block diagram reduction rules in the control system . Using the above rules you have to follow below simple steps to solve the block diagrams: 1. Combine all cascade blocks 2. Combine all parallel blocks 3. Eliminate all minor (interior) feedback loops 4. Shift The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative

cepts, such as control instrumentation diagrams and control block diagrams, are intro- duced in the next examples, it is important that you study them thoroughly. Example 1.1: Surge Tank Block Diagram Reduction Three primary situations for reducing block diagrams to simpler forms: Example #3 - Step #1 U(s) + - - a s 1 2 s 1 a 1 a 0 Y(s) + b 0 + b 1 Re-draw slightly, then close this feedback loop + Example #3 - Step #2a U(s) + - 2 1 a s a 1 + s 1 a 0 Y(s) + b 0 + b 1 Cannot have a вЂњpick-offвЂќ in middle of feedback loop! Cannot have a вЂњpick-offвЂќ in in middle of

NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 2 Information Organization through Block Diagram discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams.

A reliability block diagram (RBD) is a drawing and calculation tool used to model complex systems. An RBD is a series of images (blocks) representing portions of a system. Once the images (blocks) The use of block diagram algebra to п¬Ѓnd the system transfer function is advisable for simple systems, but for complex systems it gets quite involved. The signal п¬‚ow graph technique is employed in Section 2.4 as an alternative

discusses introductory aspects of automatic control systems, including various control actions.Then,it presents a method for obtaining block diagrams for physical systems,and, finally, discusses techniques to simplify such diagrams. Block Diagram Reduction W.3 4Masonв„ўs Rule and the Signal-Flow Graph A compact alternative notation to the block diagram is given by the signal-вЃ„ow graph introduced Signal-вЃ„ow by S. J. Mason (1953, 1956). As with the block diagram, the signal-вЃ„ow graph oвЃ„ers a visual tool for graph representing the causal relationships between the components of the system. The method consists of

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