Currently, stereotaxic brain surgery is an actively developing branch of medicine. During these operations, a special needle is inserted into the brain through a hole in the skull. This needle is moved in the brain tissue so that its tip reaches a certain point, after which the necessary medical manipulation is performed (for example, taking a puncture). To ensure accurate positioning of the needle, it is advisable to monitor the process of such operations using the magnetic resonance imaging apparatus. This puts restrictions on the type of actuators that can be used to drive the needle. The paper considers the problem of controlling the penetration of a cylindrical needle into a phantom of the brain where the control force is generated using a piezoelectric drive (PED). To describe the interaction of the needle with the tissue, a phenomenological model is proposed, under which it is assumed that the phantom tissue is a viscoelastic and plastic material, and also demonstrates relaxation properties. When describing forces acting on the lateral surface of the needle from the side of the tissue, the presence of dry friction is taken into account. The proposed model contains a number of parameters that are identified based on experiments carried out at the NCKU (Taiwan). In these experiments, a standard biopsy needle was inserted into a phantom made from agar-agar solution, and the position of the needle and the force acting on it from the tissue were registered. It is shown that the experimental results are in good agreement with the calculations in the context of the model. An algorithm for controlling the needle by setting the frequency of excitation of the probe is proposed. The aim of the control is to introduce the needle to a given depth at a given constant speed, and then hold the needle at this depth. During the process, it is required to avoid overshooting in speed and position. Numerical simulation has been carried out. The effect of the feedback parameters on the nature of the process is investigated. It is shown that the proper choice of parameters allows for avoiding the overshooting.
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