Mechanical (direct-drive) systems designed for high-speed and high-accuracy applications require control systems that eliminate the influence of disturbances like cogging forces and friction. One way to achieve additional disturbance rejection is to extend the usual (P(I)D) controller with a disturbance observer. There are two distinct ways to design, represent, and implement a disturbance observer, but in this paper it is shown that the one is a generalization of the other. A general systematic design procedure for disturbance observers that incorporates stability requirements is given. Furthermore, it is shown that a disturbance observer can be transformed into a classical feedback structure, enabling numerous well-known tools to be used for the design and analysis of disturbance observers. Using this feedback interpretation of disturbance observers, it will be shown that a disturbance observer based robot tracking controller can be constructed that is equivalent to a passivity based controller. By this equivalence not only stability proofs of the disturbance observer based controller are obtained, but it also provides more transparent controller parameter selection rules for the passivity based controller.

Several techniques exists to incorporate disturbance rejection requirements in a linear controller design. Contrary to, for example the H-infinity controller design technique where only one degree of freedom is available to obtain both disturbance rejection and performance, a Disturbance Observer adds a degree of freedom, thereby enabling a separate design of the disturbance rejection and the performance. There are many ways to design, implement and represent disturbance observers. In this paper, we focus on two design methodologies and their corresponding representations. It can be shown that, in case the (SISO) plant is linear, the methodologies result in an equivalent disturbance observer. In this paper, we will use this equivalence to relate some properties well-known for one methodology to the other methodology, and vice versa.

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