Recent Developments of Electrical Drives - Part 27. The book stating the recent developments of electrical drives, can be useful for engineers and researchers investigating and designing electrical and electronic devices as well as for students and young researchers dealing with electrical and electronic engineering, computer sciences (advanced computer modelling, sophisticated control systems with artificial intelligence tools applied, optimal design bye use of classical and genetic algorithms employed), applied mathematics and all the topics where electromagnetic, thermal, mechanical phenomena occur | II-10. Impact of Magnetic Saturation of Induction Motor 253 Taking into account equations 18 the position controller and the rotor flux linkage controller are given by 19 . va ka0e1 ka1e1 ka2e1 y1 vp kpe kP2 e2 y 19 After inserting 19 in the linearized system 15 the tracking error dynamics of the closed loop system is given by 20 e 1 ka2 e1 ka1e1 ka0e1 0 2 kp2k2 kpiC2 0 20 with k . being positive constants. The desired dynamics of the tracking errors e1 and e2 is assured by selecting the corresponding eigenvalues X . of the characteristic equations 21 . I ka2lX ka1X ka0 0 X2 kp2l kp1 0 21 Observer design The state variables of the selected IM model are necessary to realize control based on the described input-output linearization. The corresponding observer similar to the one presented in 15 is given by 22 . It is based on the electromagnetic subsystem of the two-phase is vFr state-space IM model 3 in the ap reference frame. The coefficients k . are determined in the literature 14 . I- C -I I- c d dt _ Z _ Isa s0 zv r a C Mr W _ z Isa zv s0 zv r a D Usa usp ki Mrk2 k3 Mrk2 k1 Mrk3 i- zv sa I zv lsf Isa jsft - zv -frp. zv -frp. Mrk3 k3 22 The symbol denotes the observed values. Experimental results The experiments have been performed to test the proposed input-output linearizing tracking control. The elements of the experimental system are the three-phase Semikron IGBT inverter the three-phase 3 kW IM Sever with wound rotor whose parameters are given in Appendix C and the DC motor MavilorMo2000 with an Infranor DC power converter as the dynamic load. The control algorithm was executed on the dSPACEDS1103 microcontroller board. A block diagram of the proposed IM drive s tracking control that includes magnetic saturation is presented in Fig. 2. Experiments were done using the reference value T 2 Vs 2. The smooth reference trajectories for the position 0r and the speed rnr were generated from the kinematic model and are shown in Figs. 3 a and 4 a . The step changes
