A Practical Approach To Robust Sliding Mode Control

In this thesis, important aspects of sliding mode control are investigated. Although
sliding mode control has many restrictions and drawbacks, this type of controller is attractive
because it has many powerful characteristics. In order to show the performance
and robustness of the controllers proposed in the thesis, two simulation systems and an
experimental one are studied.
In this work, a new approach to design sliding mode and observer is proposed. The systematic
way to design and tune sliding mode output feedback controller is proposed. The
design problem is solved in two steps, the first involves astate feedback and the second,
an output feedback problem. First, using null space dynamics, the sliding hyperplane
for the unmatched uncertainty is designed. Then, by tuning the sliding hyperplane, a robust
controller is constructed for the whole uncertainty; this problem takes the form of a
static output feedback problem. Based on this, a dynamic output feedback controller for
the system, augmented with the sliding hyperplane, is designed. The synthesis involves
the solution of an LMI and a BMI problem; the BMI problem is solved iteratively. The
desigu is based on rninimizing H2, Hoo nonn. This structure is extended to the LPV
system to build the LPV sliding mode controller; the controller is simulated to ADIP.
The design is achieved by first designing the fixed sliding hyperplane; then, the LPV
compensator is fed the hyperplane with necessary information about the state.
A new approach to design controller based robust observer is proposed. The controller
consists of state feedback gain fed from the observer with necessary information about
the states. The parameters of the state feedback gain and observer are designed robustly
against parameter uncertainty that can be formulated in polytopic form. This technique
does not depend on the separation principle, which is usually used to design the observer.
A new method for the synthesis and analysis of BMI is proposed for the design; the BMI
problem is solved by converting it to LMI by fixing one of the decision variables and
solving the others. In addition, based on the robust observer, a free chattering sliding
mode controller based variant sliding hyperplane is proposed. The design procedure is
also formulated for the problem in BMI formula that is solved iteratively as explained
previously. The efficiency of the methods is demonstrated by comparing them with state
feedback controller based observer, constructed using the separation principle method.
All the proposed controllers are applied successfully to the rectilinear mechanical system.
The methods for tuning the controller parameters are discussed and the rules to tune
these controllers are given. A new tuning parameter, a ,is proposcd. The influence of this
parameter on the performance and robustness of the ACC problem is shown. It also has
an important role in tuning the controller for real system. For the robust observer, the
60 is an important tuning parameter to find the feasible region with good performance
for non-convex matrix inequality.