Figure dlagral unity-feedback control system Proportional Controller Plant R(s) C(s) s(3s +1) K 5+2s +4
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- A 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)(Figure 1 One Wheel Model), Part1-(Derive equation of motion for a given system and obtain transfer function and state space representation.) , part2-(Draw closed-loop diagram for full-state- feedback controller.) , part3- (Select proper coefficient (u=-Kx) satisfying that .) part4- (Simulate the closed-loop system and show the response of it.) Note: Tahe Reference signal as With f = 0.1 Hz. !!!!!!!!! Please solve these steps, at least the first step which is writing the equations of motion of the system and the second step which is drawing closed loop diagram for Full state feedback controller.!!!!a)is the aircraft stable about the equilibrium represented by the transfer function? b) Using proportional feedback,what is the range of acceptable gains for the closed loop systen to be stable? c) Design a feedback control system that allows the pilot to command a pitch angle with overshoot less than or equal to 4.15% and a natural frequency of greater than or equal to 0.99 rad/s d) Design a feedback control system that allows the pilot to command a pitch angle with the same overshoot and a natural frequency of one half the system in part c.
- A 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?.1. Give an example of open loop and closed loop system (one example each). Also state the input, control system, feedback and output parameter. Example. 1. Open Loop - Water Heater: Input - Water Temperature (Cold) System - Heating Element Output - Water Temperature (Hot) 2. Closed Loop - Air-conditioning System Input - Desired Room Temperature Control - Motor controller/Compressor/ACU Feedback - Temperature Sensing Output - Room TemperatureFor the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)
- Calculating the separation and / or joining angles in the negative feedback control circuit, if any, given as Controlling (K) and Controlled G (s) = (s + 1) / (s2-4 * s + 5) Explanation: The roots of the equation (s2-4 * s + 5); s1 = 2 + 1 * j and s2 = 2-1 * j and the system Transfer Function is TF (s) = K * G (s) / (1 + K * G (s)). a. There are split angles up to (+108.435) and (-108.435) b. There are split angles as much as (+71,565) and (-71,565) c. There are conjunction angles of (+90) and (-90). D. There are separation angles as much as (+18.435) and (-18.435). E. There are no separation and convergence angles.The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable. The speed control of the car is represented by the model shown in Figure 2. (i). Determine the steady-state error of the system with unity gain and explain with suitable justification about the system type. A= 12 , B=5 , C=10 , D= 16 (ii). Determine the static error coefficient associated with the system. (iii). Assume the steady state error to be 10%. What will be the value of the controller gain, K?A stock-flow system models the level of water in a lake. Near a certain equilibrium point, there are three feedback loops: an amplifying feedback loop with strength of +0.55 per month, a stabilizing feedback loop with strength of -0.09 per month, and an amplifying feedback loop with strength of +0.79 per month. Calculate the strength of the overall feedback.
- Q(s) = S5 + 2S4 + 2S3 + 4S2 + 11S + 10 = 0 i). Identify the stability of the system using Routh Hurwitz Algorithm. (ii). Comment about the Roots location.The satallite system below is controlled using reaction wheels. The torque wheel input for the system is u(s) and the satallite attitude is Ө(s) For a strong communication link Ө needs to be a value where the satallite atenna is pointing at the ground station The transfer function for this system will be shown in the picture. Design a feedback control system that sets the closed loop damping ratio at 0.8 and the natural frequency is at 10 rad/sec.Given the system equipped with unitary feedback, whose direct branch transfer function is: Design a PID controller with one of the Ziegler-Nichols methods.