Part of an engineering project: Engineering Design designed for Freshmen at Songdo
Were working on a robot driving straight toward a wall. It has a distance
sensor that allows it to observe the distance to the wall at time n, ds[n],
8.2-2. Consider the system of Fig. P8 .22 with T = 02 .
(a) Show that the pulse transfer function of the plant is given by
1 = 0.018732 + 0.01752
515:1) lz 1le 0.8187j
(b) The frequency response for G(z) is given in Table P8.22. From this freq
2.3-2. (a)Write, as a series, the ztransform of the number sequence generated by sampling the time
function 9(1) 2 8 every T seconds, beginning at t = 0 . Can you express this transform in
(b)Evaluate the coefcients in the series of part (
7.2-6. Consider the system of Fig. 17725, and let the digital controller be a variable gain K such that
9(2) 2 K Hence m(kT) = Ke(kr)'
(a) Write the closedloop system characteristic equation as a function of the sample period T.
(b) Determine the ranges o
9.2-2. Consider the plant of Problem 9 .21 , which has the transfer function, from Example 9 .5,
5 52(5 + 1)
_ 0. 004842 + 0.00468
22 1.9052 + 0.905
(a) Using the poleassignment design, find the gain matrix K required to realize the cl
8.11-3.Consider the system of Problem 8.1010.
(a) Plot the root locus for this system, and find the value of K > 0 for which the system is stable.
(h) Find the time constant for the system with K = 1 .
(c) Design a phaselead controller such that the chara
6.2-1. Consider the closedloop system of Fig. P6.21.
1 2' 0.5 C)
7:25 .9 s+0.5
Figure P6.2-1 System for Problem 6.21.
(a) Calculate and plot the unitstep response at the sampling instants, for the case that 0(2) = 1