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The model of a controlled quantum system of interacting spins on the basis of the Schrödinger equation containing linear unbounded control is transformed according to the scheme known from the theory of degenerate problems to a derivative system equivalent to the original one, but regular and symmetric, which opens up new possibilities for investigation for various particular cases. A characteristic case is considered when the control action extends uniformly over all spins. In this case, the derivative system becomes the usual Schrödinger equation with impulse control only at the boundaries of the time interval. An effective algorithm for optimizing control is proposed.