Dynamic surface control-based stabilization of an n^thchained systems with application to a car-like robot

Design of LCC HVDC wide‐area emergency power support control based on adaptive dynamic surface control

“…2 and the design process of the control strategy is shown below. First, make a variable change based on the DSC to divide the whole system into two subsystems as there are two state variables in the state space of AC-DC parallel system [17,18]…”

“…x 2d is obtained through a first-order filter as shown in (11) based on the design process of DSC [17,18] and by doing this the control strategy based on DSC is simpler than the control strategy based on backstepping control…”

“…In order to stabilise (17) and deal with the parameter uncertainty, we design the virtual control rule, v, as shown in the following equation:…”

“…Considering (14), (15), (17), (19) and (23), according to the virtual control rule described by (18) and adaptive control schemes described by (19), we can obtain the time derivative of V as shown in the following equation:…”

“…As a result, the control rule is continuous. In addition, the control rule and the design process are simpler than backstepping technique [17,18]. However, the conventional DSC is not immune to parameter uncertainties, unknown modelling error and external disturbances which are common in dynamic systems.…”