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1 Direct discretization Derive the transfer functions of the discretized versions of the following systems, using...
Linear Systems (3) Write an expression for the following functions using shifted and scaled versions of the unit step function u(t)
1. For Kc = 1, derive the overall transfer function for set-point tracking. 2. For Kc = 1, derive the overall transfer function for disturbance rejection. 3. With the PI-controller settings fixed, find the stability range of the P-controller gain using direct substitution method. 4. Match the following control test to the response curves given in the following figure (eg. I – A, II – B, III – C, IV – D) The following figure shows a cascade control system...
Write the differential equations and their respective transfer functions for the following mechanical systems, ignoring friction. i) Spring -Mass ii) Spring- Damper iii) Spring -Mass-Damper iv) Spring- Mass -Damper-Damper
Please solve the question below: Required are the Bode Magnitude Plots for G(s), C(s) and G(s)C(s) AND the discretized controller in Z-transform (using Generalized Bilinear Transformation) AND Derive the Euler and Tustin discretization 2.Given a continuous control system in the following figure, the plant ()-+2) plant G(s)- and +2) the controller Ca-il.7(s +4.41) 8 + 18.4 41.7(s4.41) 18.4 4 s( 2) a). Sketch the Bode magnitude plots of the plant G(s), the controller C(s), and the controlled plant G(s)C( b)....
Problem 11: Discretization of a Continuous-Time Filter Consider the continuous-time system with transfer function Hc(s) A discrete-time approximation to the system using the [16, -8 two's complement representation scheme is to be designed (A) Using Tustin's approximation, determine a discrete-time approximation with transfer function (B) Determine the poles and zeroes of Hd,Tustin(z), noting that the poles are complex conjugates (C) Plot the frequency responses of Hd,Tustin (2) and of Hd.eract (z) Hd, Tustin (z) using the sampling time 1 ms....
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous time systems associated with state matrices (A, B, C) and (A, B,C), respectively. Thus the systems have state representations (t) = Ar(t)+Bu(t) t)C(t) 1(t y(t) and Ci(t) = Assume system (A B. C) and (A. B,C) are equivalent representations, and hence there erists an invertible matriz P such that i(t) = Pa (t) defines a coordinate transformation between the two systems...
D. Question 4 Evaluate the stability of the systems with each of these transfer functions: H(s) =-100 8+200 . H (s)=804 H(s) 15s . H(s)=7741029 2 +4s+29 3s2+12 s2-4s+29
(a) Implement the following Boolean functions using decoders. i) F1 = x'y z' + x Z ii) F2 = x y' z' + x' y (b) Implement the following Boolean function using multiplexers. i) F1 (a, b, c, d) = Σ(1, 3, 4, 11, 12, 13, 14, 15) ii) F2 (a, b, c, d)= Σ(1, 2, 5, 7, 8, 10, 11, 13, 15)
3. Determine whether the LTIC systems with the following transfer functions are BIBO stable and explain why or why not. = 2 + (8+1)(8+2) (a) Ĥ2(s) 82 +55+6 (b) A3 (8) (5-1+j5)(3-1-15) (c) Î(8) = (6+2)5+4) (d) Â14(8) 1,2716 (e) Âg(s)
2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using partial fraction expansion and determine the value of lim h(t) if the limit exists. Verify that lim- n(t)-0 for stable systems. (optional) After performing the partial fraction expansion by hand (required), yoiu are encouraged to use MATLAB to verify your results. MATLAB has a function called 'residue' that can calculate poles (pi) and residues (ci). For example, the following line will calculate the...