Indirect Sliding Mode Control with Double Integral Sliding Surface

Error in Indirect ISM-Controlled Converter . . . . . . . . . . . . 245 11.3 A Possible Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 11.4 Application of Double-Integral Sliding Surface to PWM-BasedTypes of Indirect Sliding Mode Controllers . . . . . . . . . . . . . . . . . . . . . 247 11.4.1 Double-Integral Sliding Mode Controllers . . . . . . . . . . . . . . . 247 11.4.2 Architecture of DISM Controllers in PWM Form . . . . . . . 249 11.4.3 Existence Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 11.4.4 Stability Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25311.4.4.1 Ideal Sliding Dynamics . . . . . . . . . . . . . . . . . . . . . . . 255 11.4.4.2 Equilibrium Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 11.4.4.3 Linearization of Ideal Sliding Dynamics . . . . . 25611.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11.5.1 Simulation Result of PWM-Based DISM BuckConverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11.5.2 Experimental Result of PWM-Based DISM BoostConverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259It should be quite clear by now that the actual application of SM controllers in power converters have been hindered by two major challenges: the varying operating frequency of the SM controller, and the presence of non-negligible steady-state error in the regulation due to practical non-idealities. Regarding the first issue, several methods of fixing the switching frequency, which include the incorporation of constant timing functions or circuitries into theof Switching Power35, 52], the use of strategies as discussed in Chapter 5, and the indirect implementation of the SM controllers using the PWM approach as extensively elaborated in Chapters 6 to 10, have been proposed. As for the second issue, it has been widely known that the steady-state error of an SM-controlled system can be effectively suppressed through the use of an additional integral term of the state variables in the SM controller [11, 23, 52, 55, 63, 84]. This method is known as integral sliding mode control. When incorporated, the consequence is an SM-controlled system 1) with motion equation of the same order as the original system; and 2) with i