Variable structure control of non-simple input systems

Abstract

To date the variable structure control (VSC) technique has been used to control systems that are affected by a forcing function that is composed solely of an input u (i.e. simple input systems). However, some systems are affected by forcing functions that are composed of an input plus its derivatives and integrals (i.e. non-simple input systems).

A procedure is presented that will allow control inputs to be designed lo allow the VSC technique to control the motion of such non-simple input systems. The procedure initially involves a change of variables to eliminate derivatives of the input, u. The structure of the new input variable, u, is then designed based on the number of derivatives in the description of the sliding surface, r, and the highest number of integrals of the input that appear in the forcing function, m. A procedure to find the constraints on the gains is also presented

Finally, an example is presented that involves using this procedure to design a VSC control input that can force a non-simple input second-order mechanical system to behave like a simple first-order system. The results from a simulation of this system-controller combination are also presented, lo illustrate how the input and output of the system respond to a step change in the system's reference signal.