Concept explainers
Figure P5.34 shows the diagram of au inverting operational amplifier.
FIGURE P5.34 Inverting operational amplifier
a. Assuming an ideal operational amplifier, use a similar procedure to the one outlined in Problem 52 to find the system equations.
b. Draw a corresponding block diagram and obtain the transfer function
c. Show that when
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
CONTROL SYSTEMS ENGINEERING - WILEYPLUS
- Determine the transfer function C/R for the block diagram below by signal flow graph technique. R + G₁ a G₁ G₂ H₁ H₂ G₂arrow_forward1) Obtain the Mechanical system equivalent to the above electrical System (show it as a diagram). In addition, provide the mathematical model of the obtained mechanical system. 2) What is the output of the system in terms of Matrices C and D (if exist).arrow_forward1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂arrow_forward
- 4.A system has the characteristic equation D(s) = s' + 2s² + (k+1)s+ 6 = 0 2. Find the range of K for a stable systemarrow_forwardQ2. Consider the following mechanical system, z and y are displacements and the input force to the system is u. U b m Frictions surfacearrow_forwardConsider the following mechanical system: →y k +f m (?)ap 9+ + ky(t) = f (t) dt d'y(t) dy(t) m dt? Obtain the state space model of the system with input f(t) and output y(t). Calculate the system matrices for m = 1, k = 1 and b = 2. 3.arrow_forward
- Consider the translational mechanical system as shown in Figure Q3 with two force inputs, F,(t) and F2(t) being applied on Ma and M3 respectively. Derive the equations of motion for each mass M,, M2 and M3. Then, determine the state space representation of the system if the state variables are as: X(t) = [x, (t) *(e) x2(t) i(t) x3(t) ž()]". The output of the system is taken as displacement at x, (t). X1(t) X3(t) K X2(t) F2(t) M1 M3 M2 F1(t) Figure Q3arrow_forwardObtain the transfer function for the mass-spring system represented by block diagram shown in Figure 1.21. Draw the simplified block diagram. X; (t) f(t) X, (t) k m D Figure 1.21 Block Diagram for mass-spring systemarrow_forward2. Assume the disturbance input f(t) = A sin wt is applied to the mass M. (50) Find the state space equations of the system. (15) b) Determine the transfer function of the system. (15) c) Assuming rigid k - infinite with zero weight, find the input angular frequency w to generate the exciting resonance response y. (20) (Hint : write w in terms of (M,m,K}). M x(1) ele learrow_forward
- The equation of motion of a mechanical system is 4 + 10y = 120g (t) where g(t) is dy dt the stimulus or input applied to the system and y(t) is its output. Assume the system is quiescent. i. Find the transfer function of the system and the pole. ii. If a step of unit height is applied at the input, in the Laplace domain, find the system output, y(s), using partial fractions. Hence determine the time domain output of the system, y(t). iii.arrow_forward3m i+4cx+ 2kx =4C j+3ky %3D For the system given above, obtain the state-s pace representation.arrow_forwardFigure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.arrow_forward
- 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