S’ = 0.01S − 0.00002S^2 − 0.5SZ
Z’ = 0.2SZ
R’ = 0.3SZ*
*however, R’ = 1.5Z’
Graph Do a linear stability analysis and using the jacobian find and determine the type of fixed points this ODE has.
S’ = 0.01S − 0.00002S^2 − 0.5SZ Z’ = 0.2SZ R’ = 0.3SZ* *however, R’ =...
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical points. Determine the type and the stability. . Briefly describe the overall behavior of r and y
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to...
consider the system of differential equations ; 1) Find the fixed points of the system , 2) Evaluate the Jacobian Matrix at each fixed point, 3) Classify stability of each fixed point, 4) Sketch the graph of the phase portrait,
8-24. The block diagram of a de-motor control system is shown in Fig. 8P-24. Determine the range of K for stability using the Nyquist criterion when K, has the following values (a) K0 (b) K 0.01 R(s) E(s) Y(s) 10 +0.1 0.01s Figure 8P-24
8-24. The block diagram of a de-motor control system is shown in Fig. 8P-24. Determine the range of K for stability using the Nyquist criterion when K, has the following values (a) K0 (b) K 0.01...
Problem 2 (50 pts): Consider the unity-feedback system: R(2) E(z) Y(2) K G(2) 2 G(2) = is the transfer-function of the plant and zero-order hold. (2 – 1)(z – 0.2) a) (5 points) Find the closed-loop transfer-function Hyr(2). b) (5 points) Find the characteristic polynomial. c) (20 points) Determine the range of K for closed-loop stability.
Show that the system is stable and the final answer is Z=N+P =-2-2-0, which means the system stable. Also, make sure to find Gain margin (GM) and Phase margin (PM). Digital Compensator Plant R(s) c(s) G(s) Sensor For standard system as shown bellow, the open loop frequency response is as shown on the flowing page. Use the Nyquist Criterion to determine whether or not system is stable. Determine any applicable stability margins. Be sure to solve the problem step by...
14) Consider the parallelepiped D determined by the vectors (2,-1,2), (1,3, 1), and (2,-1,1). Let T(z, y, 2)a-ytz. Consider the integral I - JSsD TdV. Using the Change of Variables Theorem, write I as an integral of the form T(r(r, s,t), v(r, s, t), z(r, s,t))lJ(r,s, t) dr ds dt for a suitable linear change of variables (r, s, t) (, y,z). The Jacobian J(r,s,t) you get here should be a constant function.
14) Consider the parallelepiped D determined by...
dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing only the first quadrant. (a) Graph the nullclines on a (b) Find the fixed points (there are two) to determine the nature of each fixed point (i.e., source, sink, saddle, and (c) Use Jacobian analysis whether it is a node or spiral). (d) Draw the flow arrows in each region of your phase plane from part (a). You may use a computer to help...
Let S be the solid of revolution obtained by revolving the region R of the z y plane about the line z 4where R is the region defined by the curves -6 andy-6- We wish to compute the volume of S by using the method of cylindrical shells a) Determine the smallest x-coordinate 1 and the largest x-coordinate r2 of the points in this region b) Let x be a real number in the interval |1,2 We consider the thin...
(10 points) Linear Programing (SLOI): 4. iven constraints. 2x+Sy subject to the g Graph the Feasible Region, and minimize the quantity z x +2y 21 r +2y s10 2 2x 2 r 20
(10 points) Linear Programing (SLOI): 4. iven constraints. 2x+Sy subject to the g Graph the Feasible Region, and minimize the quantity z x +2y 21 r +2y s10 2 2x 2 r 20
7. Consider a family of maps f :R-R, where f(r)= 2+c, cE R. a) Let c 0. Find all the fixed points of f and analyze the map by drawing a cobweb. Check stability of the fixed points b) Find and classify all the fixed points of f as a function of c. c) Find the values of c at which the fixed points bifurcate, and classify those bifurcations. d) For which values of c is there an attracting cycle...