Dynamic Sliding Mode Control based on integral manifold for MIMO

Abstract

In this study an output feedback control law
design based on sliding mode control approach for Multi
Input Multi Output (MIMO) uncertain nonlinear systems is
presented. A class of output feedback linearizable MIMO
uncertain nonlinear systems is considered to be affected by
both matched and unmatched uncertainties. The control law
design is relying on an integral manifold. The use of the
integral manifold allows us to subdivide the control law design
architecture into two steps. In the first step, pole placement
based continuous control component is designed which regulates
the system output when sliding mode is established. In the next
step a discontinuous control component is design to cope with
the uncertainty presence. In the present proposal, the control
input is applied to the actual system after passing through a
chain of integrators. Consequently, the well-known chattering
phenomenon, being caused by high frequency oscillation against
the sliding manifold, is reduced and a continuous control input
is fed into the system. This is a clear benefit in many applications,
such as those of mechanical nature where a discontinuous
control action could be inappropriate. The proposed control law
is theoretically analyzed and its performance in term of output
regulation to zero is demonstrated in the simulation.In this study an output feedback control law
design based on sliding mode control approach for Multi
Input Multi Output (MIMO) uncertain nonlinear systems is
presented. A class of output feedback linearizable MIMO
uncertain nonlinear systems is considered to be affected by
both matched and unmatched uncertainties. The control law
design is relying on an integral manifold. The use of the
integral manifold allows us to subdivide the control law design
architecture into two steps. In the first step, pole placement
based continuous control component is designed which regulates
the system output when sliding mode is established. In the next
step a discontinuous control component is design to cope with
the uncertainty presence. In the present proposal, the control
input is applied to the actual system after passing through a
chain of integrators. Consequently, the well-known chattering
phenomenon, being caused by high frequency oscillation against
the sliding manifold, is reduced and a continuous control input
is fed into the system. This is a clear benefit in many applications,
such as those of mechanical nature where a discontinuous
control action could be inappropriate. The proposed control law
is theoretically analyzed and its performance in term of output
regulation to zero is demonstrated in the simulation.