It is well established that the sliding mode control strategy provides an effective and robust
method of controlling the deterministic system due to its well-known invariance property to a
class of bounded disturbance and parameter variations. Advances in microcomputer technologies
have made digital control increasingly popular among the researchers worldwide. And that led to
the study of discrete-time sliding mode control design and its implementation. This brief
presents a method for multi-rate frequency shaped sliding mode controller design based on
switching and non-switching type of reaching law. In this approach the frequency dependent
compensator dynamics are introduced through a frequency-shaped sliding surface by assigning
frequency dependent weighing matrices in a linear quadratic regulator (LQR) design procedure.
In this way the undesired high frequency dynamics or certain frequency disturbance can be
eliminated. The states are implicitly obtained by measuring the output at a faster rate than
the control. It is also known that the vibration control of smart structure is a challenging
problem as it has several vibratory modes. So the frequency shaping approach is used to
suppress the frequency dynamics excited during sliding mode in smart structure. The frequency
content of the optimal sliding mode is shaped by using a frequency dependent compensator such
that a higher gain can be obtained at the resonance frequencies. The brief discusses the design
methods of the controllers based on the proposed approach for the vibration suppression of the
intelligent structure. The brief also presents a design of discrete-time reduced order observer
using the duality to discrete-time sliding surface design. First the duality between the
coefficients of the discrete-time reduced order observer and the sliding surface design is
established and then the design method for the observer using Riccati equation is explained.
Using the proposed method the observer for the Power System Stabilizer (PSS) for Single
Machine Infinite Bus (SMIB) system is designed and the simulation is carried out using the
observed states. The discrete-time sliding mode controller based on the proposed reduced order
observer design method is also obtained for a laboratory experimental servo system and verified
with the experimental results.
