Arbitrary Pole Placement with Sliding Mode Control

This paper considers the problem of placing all the poles arbitrarily for a linear time-invariant plant with (the linear part 00 sliding mode control. We solve this problem in two ways. In the first approach, we design a sliding mode control by specifying the desired pole locations. The closed-loop system under this control law has all eigenvalues at the desired places. In the second approach, the sliding mode control is designed from a given state feedback gain so that all the poles of the closed-loop system are placed at the same location as that of the state feedback controller. Here, we provide a necessary and sufficient condition for the existence of a linear gain using the sliding mode control to achieve the desired pole assignment. This condition is always fulfilled for the single input case whereas it is only applicable for certain multi-input scenarios that meet the conditions stated in the paper. In both the approaches, one can place the closed-loop poles with the proposed sliding mode control at any arbitrary location in the left half of the complex plane, unlike with traditional design, where m poles are at the origin with m being the number of control inputs. A numerical example illustrates the proposed design methodology for sliding mode control.