Rejection of disturbances in multivariable motion systems

Due to ever increasing demands in industry, the number of applications of multiple input multiple output (MIMO) control systems has increased drastically in the last decades. Although considerable progress has been made in the development of theoretical tools, feedback control design for MIMO systems still poses complexity issues for both academia and the practising engineer. In an effort to reduce design complexity, many aspects of MIMO systems are disregarded in most practical applications, at the cost of potential achievable performance. One of the important tasks of feedback control is the ability to reject disturbances. In MIMO systems, gain, phase, and directions play an important role in the systems ability to reject disturbances. The directional, multivariable, aspects of disturbances necessitate approaching the MIMO control problem in its full complexity. The goal of this work is to make directional aspects an integral part of MIMO control design. Herein, the focus is on applications of motion control systems. The contribution of this work is two-fold. The first contribution of this work is the development of techniques to characterize multivariable disturbances. A non-parametric component analysis method is developed to identify both the directional aspects of disturbances and the root cause (source) of disturbances in multivariable closed loop controlled systems. Indices are developed to quantify directionality of disturbances and, possibly, simplify multivariable control design. These techniques are applied to an active vibration isolation platform. It is shown how the location of sources can be recovered using only closed loop measurements. Furthermore, it is demonstrated how multivariable control design can be simplified. With this, it is demonstrated how multivariable aspects of disturbances can be interpreted physically and exploited in control design. The second contribution of the work involves the development of control design methods that take advantage from the multivariable aspects of disturbances. The focus is on systems where the plant dynamics are decoupled while disturbances may act on may decoupled parts of the plant at the same time. Methods are developed to design non-diagonal weighting filters for H1 control synthesis. Furthermore, manual frequency domain loopshaping techniques are developed for the design of centralized MIMO controllers that accommodate directions of disturbances and sensor noise. It is illustrated with several examples that, using these developed techniques, directions of disturbances and noise can be successfully integrated in control design for multivariable motion systems.