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RECENT ADVANCES IN ROBUST CONTROL – NOVEL APPROACHES AND DESIGN METHODSE Part 5

Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Neural Control Toward a Unified Intelligent Control Design Framework for Nonlinear Systems 109 Define Ax t x1 t - x2 t and Ap p - p. Then we have pt . . .-If Ax t I aTAx s BtAx s u s CtAx s p ds 0 t I C x1 s Apds t0 If the both sides of the above equation takes an appropriate norm and the triangle inequality is applied the following is obtained Ax t I aTAx s BtAx s u s CTAx s p ds Jt0 ft. . f C x1 s Ap ds Jt0 Note that C x1 s Ap can be made uniformly bounded by s as long as the estimate of p is made sufficiently close to p which can be controlled by the granularity of tessellation and p is bounded u t 1 aT supxeQ aT x TO Bt sup q Bt x TO and CT supxeQ CT x TO . It follows that Ax t s t -to aT Bt Ct p it Ax s ds Jt0 Define a constant K0 aT Bt CT p . Applying the Gronwall-Bellman Inequality to the above inequality yields Ax t s t -t0 K0s s - t0 exp J K0da ds t-t 2 s t -t0 sK0 20 exp K0 t -t0 Ks where K t -10 1 K0- exp K0 t -t0 and K TO . This completes the proof. 6. Simulation Consider the single-machine infinity-bus SMIB model with a thyristor-controlled seriescapacitor TCSC installed on the transmission line Chen 1998 as shown in Fig. 5 which may be mathematically described as follows b M-1 M f - - Po - D _ 1 - VtVTO Xd 1 - s Xe sin A 110 Recent Advances in Robust Control - Novel Approaches and Design Methods where s is rotor angle rad a rotor speed p.u. rnb 2n 60 synchronous speed as base rad sec Pm 0.3665 is mechanical power input p.u. P0 is unknown fixed load p.u. D 2.0 damping factor M 3.5 system inertia referenced to the base power Vt 1.0 terminal bus voltage p.u. V 0.99 infinite bus voltage p.u. Xd 2.0 transient reactance of the generator p.u. Xe 0.35 transmission reactance p.u. s e smin smax 0.2 0.75 series compensation degree of the TCSC and Se 1 is system equilibrium with the series compensation degree fixed at se 0.4. The goal is to stabilize the system in the near optimal time control fashion with an unknown load P0 ranging 0 and 10 of Pm. Two nominal .