Problem 1. Compute the discrete equivalent (by hand) using Backward Rectangular Rule and the associated difference...
1- Compute the discrete equivalent (by hand) using Tustin's Method for the continuous controller C(s). Let T, = 0.05 seconds. (s + 2)(8 + 0.1) (s + 10)(8 + 0.01)
Please help me in this question using MATLAB and Calculations please by hand Problem 2 Consider the causal non-linear discrete-time system characterized b difference equation: y the following n of amplitude P (i.e If we use as input x[n] to this system (algorithim) a step functio rge after several iterations to the square root of P t implements the above recursion to compute the square n)-P uIn), then yIn] will conver roots of 25, 9, 3, and 2. How many...
Problem statement: Use forward and backward difference approximations of 0(h) and a centered difference approximation of 0(h') to estimate the first derivative of f(x)- 0.x-0.15x-0.5x-0.25x +12 Problem #2 Steady-state temperatures (K) at three nodal points of a long rectangular rod as shown. The rod experiences a uniform volumetric generation rate of 5 X 10 Wm and has a thermal conductivity of 20 W/m-K. Two of its sides are maintained at a constant temperature of 300K, while others are insulated. Problem...
2 Problem 3 (25 points) Let I = ïrdz. a) [by hand] Use a composite trapezoidal rule to evaluate 1 using N = 3 subintervals. b) MATLAB] Use a composite trapezoidal rule to evaluate I using N - 6 subinterval:s c) by hand] Use Romberg extrapolation to combine your results from a) and b) and obtain an improved approximation (you may want to compare with a numerical approximation of the exact value of the integral 2 Problem 3 (25 points)...
Problem 10. If a continuous-time system's transfer function is given by G[s] = (3+3) P (2+5.55+25)(3+2and one wants to control the system with a discrete-time controller without changing the system's bandwidth, what is a reasonable sample period? 1. T = 0.001 seconds 2. T=0.1 seconds 3. T = 0.4 seconds 4. T=0.04 seconds 3. None of the above.
(d)A first-order system is described by the following differential equation +24x(t) = r(1) dī i) Discretize the system using (a) forward (Euler) approximation, and (b) backward (Euler) approximation, respectively, with a sampling time of T - 0.1 for both. Write down the two resulting systems as difference equations. 20% (ii) Check the stability of the continuous-time system described by equation (2) 10% (iii) Discuss the stability of the above two discretised systems obtained in (d(i)). Explain how to choose the...
My question is Problem 11.4-8 Thanks for your help! 11.4-8. Consider the third-order continuous-time LTI system * = Ax + Bu y = Cx 102 with A = To 0 Lo 2 0 -8 07 3 , B = -6] 0 , and C = [1 0 0]. Using Q = [800] 0 6 0, LO 0 4 R = 1.5 (a) First design a LQ controller for this continuous time-system using the MATLAB function iqr. Let the optimal controller...
Homework Problem: 1. Consider the following differential equation that governs a continuous-time system: (t) - 29/(t) - 3y(t) = 2e' - 10 sin(t) (a) 5 points: Derive the governing equation for the equivalent discrete-time system
Concert the following pid controller into discrete form using difference equation x(k) ot x(Tk) (1 0.091s (0.19s)A2) 1.9706 (1 0.091s (0.19s)A2) 1.9706
Let ?1,?2,…,??be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). a) Compute the mean and the variance of ?1 (which is the same for ?2, ?3, etc.) b) Use your answer to (a) to compute the mean and variance of ?̂ = 1/n (?1 + ?2 + ⋯+ ??), which is the proportion of “ones” observed in the n instances of ??. c) Suppose...