Problem 6: System 1: H Consider two LTI systems: System 2: H2 What are the controllability, stabilizability, observability, and detectability properties of HH2 and H2H. (Analyze for each mode.)...
Problem 2. Check the controllability and observability of the following systems by hand: 0.2 0 1 0.8 0] x + 111, y=[1 1]х -6
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H (el) LTI System 2 h2[n], H2(eje) Figure P2.37 The first system is described by the frequency response Hi(j =c-joo < 0.25% 11 0.25% < and the second system is described by <A hain) = 2 Sin(0.57) (a) Determine an equation that defines the frequency response, H(e)®), of the overall system over the range -- SUSA. (b) Sketch the magnitude. He"), and the phase, ZH(e)),...
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system is non-causal and un-stable, determine the time domain impulse response
Question 5: Consider the system: 4 28 -10 2 *60)15 -27*ces *[*]us, y=[-5 2]xV Check the controllability, the observability, the stability, the stabilizability and the detectability of the system. ok b) Determine which of the two modes of the system is not controllable. Is it possible to stabilize the system? AL) If u(t)=0, how would you choose x(0) to excite the first mode only. How would you choose x(0) to excite the second mode only. dd) Is x, = [...
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response...
Also, solve the following problem. Consider a system made by cascading two LTI systems. The first system is described by y[n] = x [n] – ax (n – 3]. The second has impulse response h (n] = {po aP [n – 3p] with ( < a < 1. Find the impulse response of the overall system.
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
12 • 171 T- (6) Figure 1 (b) Consider the interconnection of the LTI systems shown in Figure 2 below. (1) Find the impulse response h[n] of the total system. (ii) Determine and sketch the total impulse response h[n] if ht[n]= 8[n-1], h2[n] = 3u[n+4], h3[n] = -3u[n-2], and he[n] = 8[n+4]. xin that the syn] - Paragraph -
1. For each of the LTI systems below find the system output y, where h is the system impulse response and x is the system input:
1. Test the controllability and observability of the
system
2. write the MATLAB code of the solution
MECH621 FINAL PROJECT- Project The dynamics of a controlled submarine are significantly different from those of an aircraft, missile, or surface ship. This difference results primarily from the moment in the vertical plane due to the buoyancy effect. Therefore, it is interesting to consider the control of the depth of a submarine. The equations describing the dynamics of a submarine can be obtained...