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Determination of Sensors and Actuators Placements
It is important to design control systems by selecting appropriate actuator and sensor types and locations. There are several traditional methods to check the controllability such as rank of controllability and observability matrices, positive definiteness of controllability observability Gramian and PBH test. However, these tests are too restrictive due to the following problems. These tests are sensitive to parameter perturbation in certain conditions. Moreover, it only answers to the binary question of whether or not a dynamical system is completely controllable and not to the question of ”°how controllable or observable”±. It is useful to define a measure which is continuous rather than binary metric, i.e., degree of controllability(DOC) and degree of observability (DOO) and degree of disturbance rejectability(DODR). However, for a system which uses both actuators and sensor, the placement of actuator can be affected by the placement of sensor and vice versa. Therefore, the measure which can consider both controllability and observability simultaneously is proposed in research and it is called degree of compensation capability(DOCC) and degree of output noise sensitivity(DONS). DOCC is sum of the three measures of DOC, DOO and DONS. DONS is affected by the both magnitude and direction of the controllability and observability Gramians.