Concept explainers
The mathematical model that permits easy interconnection of physical system.

Answer to Problem 1RQ
Transfer function model permits easy interconnection of physical system.
Explanation of Solution
Introduction:
A mathematical model is defined as a model which describes the system with the help of mathematical concepts and language.
A control system is a group of physically connected components. In order to get the desired output by calibration, the control system can be regulated using the command. The integral part of the control system is input, output, and the system itself. For the input, the command is given. The system then processes that command and gives the final output. To study and analyse the control system, mathematical model is needed which can be used for easy interconnection of physical system. That system is the Transfer Function Model.
Transfer function model defines the relationship between system’s input and output using polynomials ratio. The denominator polynomial order represents the model order while the denominator polynomials poles represent model poles. Model zeros are the roots of the numerator polynomial. There are three parameters of transfer function model, poles, zeros and transport delays.
Conclusion:
Thus, transfer function model permits easy interconnection of physical system.
Want to see more full solutions like this?
Chapter 2 Solutions
CONTROL SYSTEMS ENGINEERING
- Q1/ For what value of x do the power series converge: 8 (-1)n-1. x2n-1 2n-1 x3 x5 = X n=1 3 Q2/ Find the Interval of convergence and Radius of convergence of the series: 8 n Σ 3+1 n=1 (x)"arrow_forwardExample-1: l D A uniform rotor of length 0.6 m and diameter 0.4 m is made of steel (density 7810 kg/m³) is supported by identical short bearings of stiffness 1 MN/m in the horizontal and vertical directions. If the distance between the bearings is 0.7 m, determine the natural frequencies and plot whirl speed map. Solution: Barrow_forwardfind the laplace transform for the flowing function 2(1-e) Ans. F(s)=- S 12) k 0 Ans. F(s)= k s(1+e) 0 a 2a 3a 4a 13) 2+ Ans. F(s)= 1 s(1+e") 3 14) f(t)=1, 0arrow_forwardFind the solution of the following Differential Equations Using Laplace Transforms 1) 4y+2y=0. y(0)=2. y'(0)=0. 2) y+w²y=0, (0)=A, y'(0)=B. 3) +2y-8y 0. y(0)=1. y'(0)-8. 4)-2-3y=0, y(0)=1. y'(0)=7. 5) y-ky'=0, y(0)=2, y'(0)=k. 6) y+ky'-2k²y=0, y(0)=2, y'(0) = 2k. 7) '+4y=0, y(0)=2.8 8) y+y=17 sin(21), y(0)=-1. 9) y-y-6y=0, y(0)=6, y'(0)=13. 10) y=0. y(0)=4, y' (0)=0. 11) -4y+4y-0, y(0)=2.1. y'(0)=3.9 12) y+2y'+2y=0, y(0)=1, y'(0)=-3. 13) +7y+12y=21e". y(0)=3.5. y'(0)=-10. 14) "+9y=10e". y(0)=0, y'(0)=0. 15) +3y+2.25y=91' +64. y(0)=1. y'(0) = 31.5 16) -6y+5y-29 cos(2t). y(0)=3.2, y'(0)=6.2 17) y+2y+2y=0, y(0)=0. y'(0)=1. 18) y+2y+17y=0, y(0)=0. y'(0)=12. 19) y"-4y+5y=0, y(0)=1, y'(0)=2. 20) 9y-6y+y=0, (0)-3, y'(0)=1. 21) -2y+10y=0, y(0)=3, y'(0)=3. 22) 4y-4y+37y=0, y(0)=3. y'(0)=1.5 23) 4y-8y+5y=0, y(0)=0, y'(0)=1. 24) ++1.25y-0, y(0)=1, y'(0)=-0.5 25) y 2 cos(r). y(0)=2. y'(0) = 0. 26) -4y+3y-0, y(0)=3, y(0) 7. 27) y+2y+y=e y(0)=0. y'(0)=0. 28) y+2y-3y=10sinh(27), y(0)=0. y'(0)=4. 29)…arrow_forwardAuto Controls A union feedback control system has the following open loop transfer function where k>0 is a variable proportional gain i. for K = 1 , derive the exact magnitude and phase expressions of G(jw). ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities. iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin) iv. what happens to the gain margin and Phase margin when you increase the value of K?you You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus NO COPIED SOLUTIONSarrow_forwardThe 120 kg wheel has a radius of gyration of 0.7 m. A force P with a magnitude of 50 N is applied at the edge of the wheel as seen in the diagram. The coefficient of static friction is 0.3, and the coefficient of kinetic friction is 0.25. Find the acceleration and angular acceleration of the wheel.arrow_forwardAuto Controls Using MATLAB , find the magnitude and phase plot of the compensators NO COPIED SOLUTIONSarrow_forward4-81 The corner shown in Figure P4-81 is initially uniform at 300°C and then suddenly exposed to a convection environment at 50°C with h 60 W/m². °C. Assume the = 2 solid has the properties of fireclay brick. Examine nodes 1, 2, 3, 4, and 5 and deter- mine the maximum time increment which may be used for a transient numerical calculation. Figure P4-81 1 2 3 4 1 cm 5 6 1 cm 2 cm h, T + 2 cmarrow_forwardAuto Controls A union feedback control system has the following open loop transfer function where k>0 is a variable proportional gain i. for K = 1 , derive the exact magnitude and phase expressions of G(jw). ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities. iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin) iv. what happens to the gain margin and Phase margin when you increase the value of K?you You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus NO COPIED SOLUTIONSarrow_forwardAuto Controls Hand sketch the root Focus of the following transfer function How many asymptotes are there ?what are the angles of the asymptotes?Does the system remain stable for all values of K NO COPIED SOLUTIONSarrow_forward-400" 150" in Datum 80" 90" -280"arrow_forwardUsing hand drawing both of themarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY





