Nonlinear and adaptive control of uncertainly known objects is one of the most difficult problems of modern control theory. Today, most of developed control algorithms and methods of is dedicated exactly to the stabilization of nonlinear systems, as evidenced by many works in international and national conferences and journals published in recent years. Nevertheless, it should be noted that universal methods of synthesis of nonlinear and adaptive control algorithms in real time do not exist.
One of the problems, on which the activity of the "Laboratory of nonlinear and adaptive control systems" is aimed, is development of universal methods and algorithms of nonlinear and adaptive control spanning a wide enough class of systems. On the other hand, one of the laboratory goals is approbation of developed methods in practice while the greatest interest is the control of objects with mathematical models as realistic as possible since majority of real robotic systems operate in conditions of external perturbations and have nonlinear and hybrid models with parametric, signal uncertainties and unreported dynamics.
A large number of papers is devoted to the control of objects under the action of an unknown multiharmonic disturbing effect while the control is performed by measurements of only the output variable and the control signal. However, despite the great variety of methods and models the problem of compensation of multiharmonic disturbances for the case when the object is non-linear and the control channel is characterized by a delay is poorly researched. To solve this task methods of compensation of sinusoidal disturbances acting on a linear control object were proposed. As a result, developed methods were distributed for the case of minimum-phase and strictly minimum-phase nonlinear control objects. The control problem of this class of systems with delay was solved for linear and linearized model objects that can have an arbitrary relative degree.
The algorithm of compensation of parametric uncertain multiharmonic perturbation acting on the nonlinear control object with arbitrary relative degree and delay in the control channel was proposed. This method was extended for the case of nonlinear systems.
Considerable attention was paid to the construction of the adaptive observer and parameter identification of multiharmonic signal including the total offset, frequency and amplitude of each harmonic. A similar task arises in solving the problem of compensation of parametrically uncertain disturbances that have a quasi-harmonic structure. This task requires consideration as a separate subtask since it is necessary to analyze the algorithm of parameters identification of multiharmonic signal available for measurement. The greatest interest are problems where the frequency or frequency of multiharmonic signal are not known. The proposed identification algorithm has a dynamic order proportional to the number of harmonics and exceeding it in three times that in turn improves the best known results. This algorithm has the adaptive properties with respect to the change of signal parameters and robust properties with respect to the irregular component signal. It is available to control the speed of convergence of the estimates to their true values by changing the parameters of the identification algorithm. The proposed identification algorithm provides an exponential convergence to zero of the error of frequency estimation for offset sinusoidal signal. Identification algorithm of parameters of shifted sinusoidal signal is extended to the case of multiharmonic function of time.
The next problem considered by the laboratory is developing of a robust output control law for a system with a degree nonlinearity. It was demonstrated that using recording in deviations can reduce this problem to the stabilization of the zero position for the system with polynomial nonlinearity. The proposed robust control law was applied in practice to the problem of temperature regulation for rapid thermal processes. Solution of the task was obtained using the method of consecutive compensator. Formulation of a restriction on the non-linearity represented as the union of sector and degree nonlinearity was made. The asymptotic stability of the closed loop system for this type of non-linearity is proved using Lyapunov functions that amplifies the earlier results.
Some projects of the laboratory are devoted to the control of multirotational unmanned aerial vehicles. Designing of control systems for such devices is accompanied by several problems: the architecture uniqueness of a single model of aircraft, the need to create fault-tolerant control systems, the need to operate in conditions close to real emergencies. During the work a mathematical model of a multirotational aircraft was obtained. Unstable motion of the multicopter was stabilized using the method of consecutive compensator. This method is adaptive and allows to control the aircraft with unknown parameters related to the design features. Despite the assumptions entered during the calculation of the object’s model robust properties of the algorithm provide stability. Thus, the control system that has a significantly lower order than analogs was developed.
Based on developed in the laboratory methods a control system of a mobile robot in conditions of parametric, functional and structural uncertainties, disturbances and delay was developed. The designed system uses solution of the problem of target uncertainty in which in contrast to deterministic problems of spatial motion with desired trajectory known in advance, the reference trajectory is given inaccurate or its analytical description is priori unknown. For generating a control signal current measurements of deviations from the path are used. Such movement corresponds to the motion of a kinematic mechanism (mobile robot) along the "physically specified" path defined by sensors. The main advantage of the proposed method is the output control of the system with unknown state vector and parameters. Designed control algorithm does not require precisely known relative degree of the control object since it is necessary to specify only the upper and the lower limits of the possible relative degree. This algorithm has been tested not only on stable models of wheeled robots, but also on an unstable model of a two-wheeled balancing robot. Experimental testing has demonstrated high efficiency and operability of the proposed methods.