A fully actuated system can execute any joint trajectory. However, if a system is under-actuated, not all joint trajectories are attainable. The authors have actively pursued novel designs of under-actuated robotic arms which are both controllable and feedback linearizable. These robots can perform point-to-point motions in the state space, but potentially can be designed to work with fewer actuators, hence with lower cost. With this same spirit, the technical note investigates the property of differential flatness for a class of planar under-actuated open-chain robots having a specific inertia distribution, but driven by only one or two actuators. This technical note addresses the following theoretical question: what placement of one or two actuators will make an n-DOF planar robot differentially flat if it is designed so that its center of mass always lies at joint 2?
This note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state-delayed discrete-time systems with norm bounded uncertainties using the concept of guaranteed cost control. Expansion-contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved, including conditions on the equality of guaranteed performance bounds. The controllers are designed in the expanded space using a linear matrix inequality (LMI) delay independent procedure specifically adapted to this class of problems. The designed controllers are then contracted and implemented into the original system. The results are specialized for the overlapping decentralized control design. The method enables an effective construction of block tridiagonal controllers. A numerical illustrative example is supplied
This note deals with the problem of regulating the displacement and velocity of a mechanical system that includes a Bouc-Wen hysteresis model both of which have uncertain parameters. The dynamic part of the hysteresis is not accessible to measurement and acts as an uncertain dynamic. It is shown that the global boundedness of the control and closed loop signals along with asymptotic regulation can be assured using a simple PID controller.
A generalized structure of complementary matrices involved in the input-state-output inclusion principle for linear time-invariant systems including contractibility conditions for static state feedback controllers is well known. In this note, it is shown how to further extend this structure when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion/contraction transformation matrices. Explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion/contraction transformation matrices. Moreover, these conditions are further specialized for a particular class of transformation matrices.
The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is supplied
This paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design