Electrical circuits with state-feedbacks are addressed. It is shown that by suitable choice of the gain matrices of state-feedbacks it is possible to obtain the closed-loop system matrices with nilpotency indices equal to two and their state variables are linear functions of time. The considerations are illustrated by linear electrical circuits.
The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of an electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.
In this paper, the issue related to control of the plant with nonconstant parameters is addressed. In order to assure the unchanged response of the system, an adaptive state feedback speed controller for permanent magnet synchronous motor is proposed. The model-reference adaptive system is applied while the Widrow-Hoff rule is used as adjustment mechanism of controller’s coefficients. Necessary modifications related to construction of the cost function and formulas responsible for adjustment of state feedback speed controller’s coefficients are depicted. The impact of adaptation gain, which is the only parameter in proposed adjustment mechanism, on system behaviour is experimentally examined. The discussion about computational resources consumption of the proposed adaptation algorithm and implementation issues is included. The proposed approach is utilized in numerous experimental tests on modern SiC based drive with nonconstant moment of inertia. Comparison between adaptive and nonadaptive control schemes is also shown.