controllable canonical form

CE2.2a Use the numerical parameters in Table 2.4 for this and all ensu- ing CE2 assignments (see Figure 1.15). Simulate and plot the open-loop state variable responses for three cases (for this problem use the state-space realizations of CE1.2b); assume zero initial state for all cases [except Case i(b) below]: i. Single-input, single-output: input f () and output O(f). (a) unit impulse input f () and zero initial state. (b) zero input f () and an initial condition of e (0) = 0.1 rad (zero initial conditions on all other state variables). ii. Single-input, multiple-output: impulse input f() and two outputs w(t) and e(t). iii. Multiple-input, multiple-output: two unit step inputs f() and r() and two outputs w() and e(1). Simulate long enough to demonstrate the steady-state behavior. What are the system eigenvalues? Based on these eigenvalues and the physical system, explain the system responses. TABLE 2.4 Numerical Parameters for CE2 System Parameter Value Units Name kg cart mass - kg pendulum mass L 0.75 m pendulum length 9.81 m/s2 gravitational accelerationProblem 1: For the following transfer function s2 + 2s + 3 G(S)= $3 + 5s2 + 8s + 4 a. Obtain the state space representation in controllable canonical form. b. Obtain the state space representation in observable canonical form. c. Repeat parts a & b using MATLAB. Problem 2: Given the following transfer function s+9 G(S) = $2 + 3s + 2 Find the state space representation and draw a block diagram for the system in the following forms a) Controllable Canonical Form. b) Observable Canonical Form. c) Diagonal Canonical Form. Repeat a and b using MATLAB.The state space representation 5 1 0 -3 0 -20 0 y = [0 1 0]x is in which canonical form? O Observer canonical form O Control canonical form O This representation is not a canonical form_ Which one is correct about randomized experiments? Check all that apply 3 It is impossible to run randomized experiments in social sciences. \"1 It is impossible to run a perfect randomized experiment. so randomized experiments are useless Although randomized experiments are impossible in some cases, it is always informative to think about an \"ideal\" experiment, whenever we study causal effect of one variable on a variable of interest. \"3 Randomized experiments are so valuable that justies spending huge amount of money. whenever it is possible. Question 11 (1 point) The RAND Health Insurance Experiment and the Oregon Medicaid Experiment are examples of discontinuity analyses non-random experiments O qualitative studies randomized experiments