1. Eigenvalues (Rad/Sec) -200 -38,29 -4.1/-7.1 1.3 -2.1 -0.1 -0.3j Modes EnginePressure EngineTemperatures EngineFan/CompressorSpeeds UnstableShortPeriod Stable ShortPeriod PhugoidMode
2. 0
3. As an example, Fig. 5 presents the bounds specified on the (1,1) element in T,(j(u). These bounds reflect the normalized units (see Tables 2 and 3). The (1,1) element of Tj(jco) corresponds to the pitch response from pitch command, 0/8c. Fig. 5 shows that the bandwidth should be approximately 3 rad/sec. Recall from Table 1, the unstable eigenvalue is at 1.3 rad/sec, and corresponds to the short period mode. In order to stabilize this mode, the bandwidth of thepitch loop should be at least 1.3 rad/sec. 1 Further note that below 3 rad/sec, the difference between the lower and upper bounds is approximately 1 to 2 rad/sec. It is considered here that these are reasonable tolerances for tracking performance. Beyond 3 rad/sec, the difference between thelower andupper bounds grows larger. This is consistent with typical performance specifications. As the system response rolls off, the upper and lower allowablebounds are not as stringent. 10-2 102 100 101
4. ITU21(1,2)I = ITU21(1,3)I 10-2 10-1 100 101
5. From Eq. (9), the singular value bounds onT,(jco), T12(jco) and T21(jco) can be derived from the matrices TL(co) and Tj/co). These singular value bounds are presented in Fig. 7. Fig. 8 presents the bounds specified for acceptable engine performance. Since the engine is modeled here as a single loop system, LB2(co) and UB2(co) are directly taken to be ITL2(co)l, and ITU2(co)l, respectively (see Eq. (9)). Fig. 8 shows that the closed-loop engine subsystem should accurately track fan speed commands out to a bandwidth of approximately 3 rad/sec. Therefore, note from Fig. 7 that the bandwidths of the airframe and engine subsystemsare approximately thesame. 10-2 10-i 100 101