Suppose we have a simple mass-spring-damper system.
The governing equation of this system is
(3)
Taking the Laplace transform of the governing equation, we get
(4)
The transfer function between the input force and the output displacement then becomes
(5)
Let
m = 1 kg b = 10 N s/m k = 20 N/m F = 1 N
Substituting these values into the above transfer function
(6)
The goal of this problem is to show how each of the terms, , , and , contributes to obtaining the common goals of:
Open-Loop Step Response
Let's first view the open-loop step response. Create a new m-file and run the following code:
s = tf('s'); P = 1/(s^2 + 10*s + 20); step(P)
The DC gain of the plant transfer function is 1/20, so 0.05 is the final value of the output to a unit step input. This corresponds to a steady-state error of 0.95, which is quite large. Furthermore, the rise time is about one second, and the settling time is about 1.5 seconds. Let's design a controller that will reduce the rise time, reduce the settling time, and eliminate the steady-state error.
please use MATLAB, screenshot the code and the plots. Answer all parts. Laboratory description: The speed...
Please answer all the questions with MATLAB and also upload the code. Thanks. 3 Experiment - Matlab controller complexity and steady-state 3.1 Consider the satellite-attitude control problem shown in following figure where the normalized parameters are J 10 spacecraft inertia; N-m-sec2 /rad erreference satellite attitude; rad actual satellite attitude; rad Hy 1 sensor scale; factor volts/rad Hr = 1 reference sensor scale factor ; volts/rad w= disturbance torque: N-m H, D(s) Js Figure 4: Satellite attitude control Suppose kP =...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...
PLEASE USE MATLAB TO ANSWER ALL OF THE PARTS. PROVIDE MATLAB CODE FOR EACH OF THE PART. PUT THE ANSWER IN A BOX. Consider the unity feedback system depicted in Figure 1 G(s) R(s) 50K s(s + a) Figure 1 1. Determine the system's closed loop transfer function. 2. Plot the system's step response for K=10 and: • a= 2 • a=5 • a= 10 3. What happens to the system's response as a increases? Justify your answer. 4. In...
Solve C & D please slide 3 is the one with the pendulum ...use the Matlab command C pid (Kp, Ki, Kd, Tf) to create your PID controller for Tr 0.5, KI = Kp = 0.5, and 1 < Kp < 10. c. (20 POINTS) REFER TO SLIDE 3: Create your frequency-domain plant as a state-space object, such that Mss1 ss (A,B,C,D) where D = 0.Similarly, Mss2 = ss (GC) d. (20 points) Use the feedback command to connect your...
PLEASE DO IN MATLAB Problem 8 (PID feedback control). This problem is about Proportional-Integral-Derivative feedback control systems. The general setup of the system we are going to look at is given below: e(t) u(t) |C(s) y(t) P(s) r(t) Here the various signals are: signal/system r(t) y(t) e(t) P(s) C(s) и(t) meaning desired output signal actual output signal error signal r(t) y(t) Laplace transform of the (unstable) plant controller to be designed control signal Our goal is to design a controller...
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Please wriite the matlab code of the question :))) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1·G,(s)-K (proportional (P) controller) 2·G,(s)=K/s (integral (I) controller) 3. G (s) K(1+1/s) (proportional, integral (PI) controller) The system requirements are Ts < 10 seconds and P.。. 10% for a unit step response. (a) For the (P) controller, write a piece of MATLAB code to plot root locus...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
10 Q.1 Figure Q1 shows a speed control system where Gi(s) 0.5s 1' and K(s)kp K(s) G,(s) Figure Q1: Speed Control System a) Determine the transfer function from d to y (4 marks) (b) Assuming the reference is zero, what is the steady-state error (e-r - y), in this case, you want yss since r 0) due to an unit step disturbance in d? What must the value of k be in order to make the steady-state error less than...
Please use MATLAB, screenshot code and results An automotive power train control system is described by the following matrix equations 1-12 -10 -57 [1] x= 1 0 0 +0 u To 100 y(t) = [ 35 – 5]x where u = -KX+r, and r is a unit step input. Use MATLAB/SIMULINK to plot different responses of the system output Y for the following feedback control gain matrix K: Casel: K = [1 44 67] Case2: K = [10 44 67]...
4. Consider the position control of a rigid body, Figure, where u(t) is the control force. An analog PID control law is described as de u)kpe)k kije0)dt; e({)= x4C)x) dt 0 kp. ky only a position sensor is available. are controller gains. Also, xq (t) is the desired position of the mass. It is assumed that kJ where and Derive a difference equation for the implementation of this PID control law on a digital computer. Use backward difference and trapezoidal...