In this paper, the authors present the synthesis of control laws for the flexible joint manipulator to stabilize the oscillation and track the desired trajectory. To solve this problem, the article applies synergetic control theory. In synergetic control theory the desired values are impressed as invariants. So the invariants act as the control objectives of the system and our task is to find the control laws for them. Using this theory, the control law is designed to ensure the movement of the closed-loop system from an arbitrary initial state into the vicinity of the desired invariant manifold, i.e. the objective attracting manifold. Thereby, not only reach the necessary invariant but also ensure the asymptotic stability of the entire system. The quality of the proposed control law is shown through simulation results on Matlab and its efficiency is shown by comparison with backsteping control law.

The article is devoted to the motion analysis of a highly maneuverable mobile robot with four omniwheels, taking into account the conditions for the appearance of wheel detachment from the surface, and the occurrence of wheel slipping. Within the motion analysis the task of determination support reactions for a mobile robot is considered. To solve this task, the design of a mobile robot is presented in the form of the frame with rods. To disclosure the static indeterminacy of the considered system the forces method is used. Dependences of support reactions from the position of the center mass are obtained. The feature of the considered system is that the obtained dependencies of the support reactions are nonlinear. Based on the obtained dependences of the support reactions, the influence of the position of the center of mass of a mobile robot with four wheels on the occurrence of detachment and slipping of wheels of a mobile robot was considered. Investigation was carried out within the framework of the dry friction model, according to which module of the friction force proportionally depends on the support reaction acting on the wheel from the side of the motion surface. Simulation was carried out, as a result of which the conditions for the position of the center of mass of a mobile robot were determined, in which wheels of a mobile robot do not detach from the motion surface, and there is no wheel slipping.

The control plant is a trolley of a single-girder overhead crane designed to move a suspended payload along the span. Features of the plant: one control with two degrees of freedom, the uncertainty of mass-inertial characteristics, and the action of non-smooth uncontrolled disturbances. We consider the reduced dynamics of the DC motor in the mathematical model, where the power supply voltage of the armature circuit is a control. Here, parametric and external disturbances affecting the mechanical subsystem become unmatched (i.e., they act through different channels with control) and cannot be directly compensated. This paper considers two main problems, each of which uses S-shaped smooth sigmoid functions with saturation. The first problem is to design the trajectory of the trolley considering the design constraints on its velocity and acceleration. Tracking such a trajectory should ensure the smooth transfer of the payload in a given time and the damping of its oscillations. For this purpose, a reference trajectory has been developed in the form of the sum of a sigmoid function and an integral of the swing angle. The proposed solution is not inferior in the efficiency to existing analogs, while its implementation requires less computational costs. The second problem is to develop a robust tracking system. For this purpose, a procedure for block synthesis of discontinuous true control and sigmoid fictitious controls (local feedbacks) has been developed. The latter are smooth analogs of discontinuous control and make it possible to suppress unmatched disturbances with a given accuracy without identifying them. In contrast to standard linear local feedbacks, the boundness of sigmoid fictitious controls does not lead to a large overshoot of state variables, which is critical in the presence of design constraints. In addition, such fictitious controls are implemented in mechanical plants and do not contribute to the wear of the actuator, which inevitably occurs when discontinuous fictitious controls are used. We presented the results of numerical simulation and carried out a comparative analysis of closed-loop systems with various fictitious controls: linear, discontinuous, and sigmoid. The results of the numerical simulation demonstrated the effectiveness of the developed approach.

The paper proposes a hybrid model for predictive control under step disturbances that lead to a sharp jump in the state of the process. Similar changes occur when controlling the temperature of the steel strip on continuous hot-dip galvanizing units. Periodic changes in strip gauge or strip speed result in abrupt changes in the temperature of the steel at the outlet of the annealing furnace. During such periods deviation control is difficult requiring introduction of tolerances that limit productivity and leading to excessive heating of the metal. The paper shows that the existing proposals for controlling the temperature of the steel strip are not effective enough with a sharp change in the state of the process. The reasons for this are unknown disturbances operating in a wide frequency range and having low-frequency and trend components, as well as many influencing factors. It is shown that the problems of representativeness of the initial accumulated data make it difficult to create complex empirical models, and the level of uncertainty of the processes in the furnace makes it difficult to create complex interpretable models. The proposed hybrid model involves combining two types of simplified interpretable process models, as well as an empirical model based on an artificial neural network. The errors of the interpreted models are shown to be effectively predicted by a neural network in the presence of an additional signal from an observer of unknown disturbances. Computational experiments carried out on the data of one of the units of MMK PJSC in Russia showed that the hybrid model provides high accuracy of steel strip temperature prediction during technological disturbances and does not require frequent reconfiguration.

For the fourth-order model of the lateral motion of an aircraft with two controls, analytical expressions for the laws of stabilization control are obtained, which ensure the optimal placement of the poles. The synthesis is based on a two-level decomposition of the control object and the method of modal control of MIMO systems developed earlier by the authors with the optimal placement of the poles of a closed control system. The method is based on the features of quadratic control obtained by solving the nonlinear Lurie-Riccati matrix equation. In this case, for the optimal controller, it is necessary that the closed control object be asymptotically stable, and the matrix obtained by the product of the matrix of feedback coefficients by the control matrix of the dynamic plant must be positive-definite symmetric. Using this approach, final analytical expressions for the matrix of feedback coefficients are obtained and, accordingly, they can be used for any aircraft that has the same structure of its own dynamics and control matrices. The results of modeling the stabilization of the lateral motion of an aircraft using the obtained analytical control laws that ensure the optimal placement of the poles and, accordingly, the control laws using the decomposition method of synthesis with the same dynamic properties in the form of the value of the poles of a closed control system are presented. These properties correspond, as in the first case, to the optimal values of the placed poles. A comparison of transient processes by components of the maximum deviation of the controls shows that with optimal control, the maximum deviation of the rudder is 1.5 times less than with control using the standard decomposition method. All other parameters of the transient process, both in terms of the components of the state vector and the control vector, are approximately the same.

The article is devoted to the development of a method for improving the accuracy of a gyro with a spherical ball bearing suspension operating in the mode of a deflection angle meter of the base on which it is installed. When operating a gyroscope as part of an information-measuring and control system, such an operational characteristic as the accuracy of readings, depending on the noise component of the gyroscope output signal, is of decisive importance. The purpose of the article is to solve the problem of reducing the noise component of the output signal while maintaining a wide bandwidth of the device and a minimum phase delay of the output signal in relation to the measured value. The paper provides an overview of the existing device construction schemes. A mathematical description of the functioning of the gyroscope is presented, on the basis of which the transfer functions for the moment (disturbing, controlling or total) along the direct and cross channels are obtained. Transfer functions are also obtained, which are the ratio of the output signal to the measured value through direct and cross channels. It is noted that the predominant frequencies of the noise component of the output signal correspond to the rotational frequency of the gyroscope rotor, the rotation frequency of the gyroscope rotor and the multiple rotation frequencies of the gyroscope rotor. The structure of the system is proposed in which the signal from the gyroscope angle sensor with a spherical ball bearing suspension is summed up with the output signal of an additional angular velocity sensor according to the corresponding coordinate and then the total signal is smoothed using an aperiodic link of the first order. The results are obtained for determining the parameters of the channel of the angular velocity meter, at which it is possible to compensate for the bandwidth limitations in the channel of the angle measurement due to the time constant of the smoothing filter and at the same time ensure effective suppression of the noise component of the output signal. The proposed construction scheme of the meter provides attenuation of noise components in the output signal of a gyroscope with a spherical ball bearing suspension at a rotation frequency of the gyroscope rotor 250 Hz by 156 times, at a frequency of nutation oscillations of the gyroscope rotor 404 Hz by 256 times, at a frequency of 500 Hz by 316 times, at a frequency of 750 Hz by 474 times, at a frequency of 1000 Hz by 630 times, at a frequency of 1250 Hz by 785 times while maintaining a wide bandwidth of 285 Hz when measuring an angle with a phase lag of the output signal from the measured one close to zero degrees in the bandwidth.