Concept explainers
Given the unity feedback system of Figure P6.3 with [Section: 6.4]
a. Find the range of K for stability.
b. Find the frequency of oscillation when the system is marginally stable.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Control Systems Engineering
- The state X(t) of a dynamical system is solution of equation 10x (t) + 30ax(t) = 40, with a = 13. Calculate the rise time of the response.arrow_forwardA satellite single-axis amplitude control system can be represented by the block diagram is as shown in Figure 2.11. The variable k, a and b are controller parameters, andj is the spacecraft moment of inertia. Suppose the moment of inertia is J=7.8E+08 (slug-ft), and the controller parameters are k=10.8E+08, a=1.5 and b=8. Spacecraft Rotational R(s) Controller motion C(s) k(s + a) (s + b) js? Figure 2.11 A negative feedback control system a) Develop an m-file script to compute the closed loop transfer function. b) Compute and plot the step response to a 10° step input. c) The exact moment of inertia is generally unknown and any change slowly with time. Compare the step response performance of the spacecraft when J is reduced by 25% and 60%.arrow_forward6. Consider the mechanical system shown in Fig. 8. Let V(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. B m V₁(t) Figure 8: A mechanical system with an across-variable sourcearrow_forward
- P4. The open loop transfer function of a unity feedback system is given by G (s) = K s(as+1)(Bs+1) Determine the range of K for stability in terms of a and B.arrow_forwardConsider in Figure 1 = 0. Iff, the translational mechanical system shown P4.17. A 1-pound force, f(t), is applied at 1, find K and M such that the response is characterized by a 4-second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? [Section: 4.6] 1+ 270 Karrow_forwardA Block diagram of a feedback control system is shown in Figure Q3. Using the Block Diagram Reduction Method, solve for the output Y(s) when:(i) Input D(s) = 0,(ii) Input R(s) = 0,(iii) Input R(s) and D(s) are both applied (i.e., R(s) ≠ 0 , D(s) ≠ 0).arrow_forward
- Consider the following mechanical system: k m +f b d²y(t) +b- dy(t) + ky(t) = f (t) m %3D dt? 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. Check the stability by using the second method of Lyapunov. 3.arrow_forwardA vibrating spring-mass system has the feedback control system shown in Fig Q3 below. (figure attached as image ACT)If K = 12.25 determine:6.1 the transfer function ; (3)6.2 the characteristic equation with a impulse input; (1)6.3 the un-damped natural frequency of the system; (2)6.4 the damping ratio; (2)6.5 the damped natural frequency; (2)6.6 the maximum percentage overshoot; (2)6.7 the peak time; (1)6.8 the settling time for the response within 2%. (2)arrow_forward• The unity feedback control structure has the following block diagram: w C(s) P(s)arrow_forward
- The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by 85 + 2s4 + 2s3 + 4s² + 11s + 10 Comment on the stability of the system. Neutral Stable Unstablearrow_forwardFigure Q2 shows the block diagram of a unity-feedback control system Proportional Controller Plant R(s) C(s). s(3s +1) 5+2s² +4 K 2.1- Determine the characteristic equation. 2.2- Using the Routh-Hurwitz criterion to determine the range of gain, K to ensure stability and marginally stability in the unity feedback syste m.arrow_forwardA system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.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