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In navigation applications, it will often be the case that we have multiple interconnected systems, each of which is modeled by a set of state space equations. For design and analysis, we want to develop a single state space model for the overall interconnected system. This is achieved by the process of state augmentation. This section rst describes the state augmentation process for two systems interconnected in the series con guration of Figure 3.2. From that discussion, the process should become clear and the reader should be able to extend the method to a larger number of systems interconnected in more general ways (e.g., parallel, feedback). In Figure 3.2, the rst system is represented as M1 and the second system as M2 . Let the rst system have the state space model x y1 = F1 x + G1 u1 = H1 x (3.22)
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Complete the following activities using problem-solving skills and your knowledge of AutoCAD. 1. The drawing in Fig. 10-9 represents a variation of a magnet for a new motor design. Draw the magnet. Select the appropriate drawing unit of measurement, drawing area, and object snap modes. Do not include dimensions, but save the drawing as magnet.dwg.
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Bockground. Engineersand scientistsoften deal with systemsthat oscillateor vibrate.As might be expected,sinusoidalfunctions play a fundamentalrole in modelingsuch problem contexts. In this discussion, will usethe term sinusoidto represent we any waveformthatcanh describedas a sine or cosine.There is no clear-cut convention for choosing either function, and in any case,the results will be identical. For this chapter,we will use the cosine,which is expressedgenerally as * f (t) : As * Cv cos(a-rst d) (14.14)
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We morph the first equation as follows: x=y z 7 x y = z 7 x y + z = 7 Next, the second equation: y = 2x + 2z + 2 2x + y = 2z + 2 2x + y 2z = 2 Finally, the third: z = 3x 5y + 4 3x + z = 5y + 4 3x + 5y + z = 4 Now we have this set of equations representing our three-by-three linear system: x y + z = 7 2x + y 2z = 2 3x + 5y + z = 4 2. Before we write down the matrix, we must be sure we have the correct signs for the coefficients. Subtraction of a positive is equivalent to addition of a negative. With that in mind, we can pigeonhole the coefficients into the matrix form:
Currently, 22 major shipyards are operational in the United States. Drafters specializing in ship design work closely with naval architects and marine engineers to design the machinery ships need to operate prop-
along venous channels also explains how an abscess may sometimes form at a considerable distance from the primary focus in the middle ear or paranasal sinuses. About one-third of all brain abscesses are metastatic, i.e., hematogenous. A majority of these are traceable to acute bacterial endocarditis or to a primary septic focus in the lungs or pleura, as indicated above. Other metastatic abscesses are traceable to a congenital cardiac defect or pulmonary arteriovenous malformation that permits infected emboli to bypass the pulmonary circulation and reach the brain. Occasional cases are associated with infected pelvic organs, skin, tonsils, abscessed teeth, and osteomyelitis of noncranial bones. Only rarely does an acute bacterial meningitis result in a brain abscess. In about 20 percent of all cases of brain abscess, the source cannot be ascertained. Metastatic abscesses are usually situated in the distal territory of the middle cerebral arteries, and they are frequently multiple, in contrast to otogenic and rhinogenic abscesses (Fig. 32-1). Also, almost all deep cerebral abscesses for example, those within the thalamus have a systemic source. It should also be noted that the clinical and radiologic features of a solitary abscess may mimic those of a brain tumor. In regard to brain abscess, careful distinction should be made between the neuropathologic effects of subacute and acute bacterial endocarditis. Subacute bacterial endocarditis (SBE), i.e., the type caused by the implantation of streptococci of low virulence (alpha and gamma streptococci) or similar organisms on valves previously damaged by rheumatic fever or on a patent ductus arteriosus or ventricular septal defect, seldom gives rise to a brain abscess. The cerebral lesions of SBE are due to embolic occlusion of vessels by fragments of vegetations and bacteria, which cause infarction of brain tissue and a restricted in ammatory response around the involved blood vessels and the overlying meninges ( cerebritis ). The cerebral symptoms of a stroke may be the rst clinical manifestations of the disease. The CSF contains a moderate number of polymorphonuclear leukocytes and frequently red cells as well, but the glucose content is not lowered and suppuration in the brain or in the subarachnoid space does not occur. It is theorized that the chronicity of the streptococcal infection allows the body to develop immunity to the organisms. The meningeal pleocytosis is occasionally associated with headache, stiff neck, and rarely with alterations of consciousness. Over time, the in amed artery may form an aneurysm (mycotic aneurysm) that later gives rise to parenchymal or subarachnoid hemorrhage (see page 727). In contrast, the more fulminant acute bacterial endocarditis i.e., the type caused by Staph. aureus, hemolytic streptococcus, gram-negative organisms, or the pneumococcus (organisms that may involve previously normal valves) frequently gives rise to multiple small abscesses in the brain and other organs of the body. Purulent meningitis may also develop, or there may be infarcts or meningocerebral hemorrhages and, infrequently, ruptured mycotic aneurysms. Rarely do the miliary abscesses progress to large ones, as illustrated in Fig. 32-1. Rapidly evolving cerebral signs in patients with acute endocarditis (delirium, confusional state, mild focal cerebral signs) are nearly always caused by embolic infarction or hemorrhage. It should be mentioned that anticoagulation has not been shown to reduce the incidence of embolization from endocarditis. In patients with endocarditis on a prosthetic heart valve, anticoagulation may be continued, but cautiously, and this treatment is suspended if there is a hemorrhagic brain infarction. It is estimated that about 5 percent of cases of congenital heart
'-----------------------------------------------------------------------------------------------------------------------------' Name : motor-test.bas ' Compiler : PicBasic Pro - MicroEngineering Labs ' Notes : Program to test the leg motors '-----------------------------------------------------------------------------------------------------------------------------' PortA set as outputs. pins 0 and 1 inputs trisa = %00000011 ' PortB set as outputs. pin 1 input. trisb = %00000001 '-----------------------------------------------------------------------------------------------------------------------------' initialize variables include "modedefs.bas"
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