Synthesis of the Decentralized Control System for Robot-Manipulator with Input Saturations

It is discussed the problem of synthesis of the decentralized adaptive-periodic control system for two degrees of freedom robotic manipulator which have an input limitations. The solution of the problem is based on the use of hyperstability criterion, L-dissipativity conditions and dynamic filter-corrector. Keywords—adaptive control; combined regulator; serial dynamic corrector; hyperstability criterion; input saturation INTRODUCTION Control systems for robotic manipulators of various purposes have a special place among the variety of modern automatic system. The relevance of the design and development problems of this class of the control systems is due to a very wide application of robots-manipulators. These devices are used in the metallurgical industry, aviation and automotive industry, chemical manufacturing and other areas [1 – 4]. As a rule, the role of the manipulators is to implement a large number of cyclically repeating process steps and problems of the development of robot control systems are to ensure the high precision tracking of a given movement trajectory. At that in practice the desired movement often has a complicated shape, which is typical for automatic arc welding of the complex compounds, laser or plasma cutting, gluing of the various component products and other. From this point of view manipulators control systems are assumed to be the class of so-called periodic control systems From this point of view manipulator control systems is assumed to be the class of socalled periodic control systems, the construction of which is expedient to use a specialized block –periodic signals generator [5 – 10]. It should be note that the robotic manipulators as a control plants are multidimensional (multiply connected) systems with set of input and output signals (each input and output signal corresponds to a single degree of freedom). In several articles which devotes to the development of complicated multiply connected dynamic plants control systems, it is proposed to use the principle of the decentralized control [11 – 13]. This approach lies in the partition of the original multi-dimensional system into several independent or interrelated local subsystems, and the stability analysis of each of them. It is well known that the development of automatic control systems is associate with a number difficulties. During the operation of practically any control system some of the control plant parameters are subject to change (for example, because of wear of its components or the external influence: changes in temperature, pressure and humidity. These parametric changes could lead to reduce of the system performance. In this context, the control algorithms development should always be carried out considering the level (or the class) of a priori uncertainty of the controlled plant. Moreover, in practice operation of the control objects takes place in the conditions of the continuous action external disturbances, which also must be considered in order to reduce their negative impact on the functioning process of the control system. One more important peculiarity is what in almost all actual systems there is a so-called input saturation, caused by the necessity of limiting the actuators input signals levels. As applied to the manipulation robots, the need to limit the input signals arises in situations when manipulator links are moved in a closed space and thus the amplitude of the control moments must have the prescribed limits which exclude undesirable robot elements displacement (for example, hitting the manipulator of the constructs that are limit the scope of its movement). It should be noted that taking account of the input limitations when developing of the control systems is a very important requirement, because in the systems which designed without considering of the input saturation in some cases there may be observed the deterioration in quality of their functioning or even loss of working capacity [14]. One of the design techniques of control systems for dynamic plants which operate in the conditions of a priori uncertainty, an external perturbations and input saturation is the use of adaptive regulators. By now it is known quite a wide spectrum of adaptive control systems schemes which are designed taking into account the input saturation [15 – 19]. In particular, in [17 – 19] for single channel plants in the assumption of complete measurement of the state vector and the absence of external noise have been proposed a variety of adaptive control schemes in the circuit with the reference model. The obtained results allowed to achieve the convergence of control error to zero, and boundedness of all signals of the closed system. The main feature of the developed control systems is the introduction of a special regulator switch which is responsible for changing the adaptive coefficients The work was supported by the Russian Foundation for Basic Research (project 17-08-00871). IT in Industry, vol. 6, 2018 Published online 17-Feb-2018 Copyright © Eugenie, Evgeniy 2018 28 ISSN (Print): 2204-0595 ISSN (Online): 2203-1731 adjustment speed, whereby the input saturation is partically or completely compensated. In [20] with the help of hyperstability criterion and L-dissipativity conditions for the scalar plant with the input saturation and the relative order greater than one has been proposed a modification of the adaptive regulator, which allowed to implement effective compensation of limitations on the entry in a non-zero initial conditions, constant external disturbances and unavailability of internal states. In the present article by using the results of [7 – 10, 13, 20 – 24] we discussed the possibility of using a combined regulator structure, as well as proposed in [20] modified adaptive algorithms for the construction of control system for two degrees of freedom robot-manipulator with input saturation. INITIAL DESCRIPTION OF THE CONTROL SYSTEM The dynamics of the manipulator, which consist of n-links and having an input saturation, according to [4], is described by ), ( ) ( ) , ( ) ( τ S f q G q q q C q q M dis = + + + & & & & (1) where q ∈ R is the vector of coordinates (angular displacement) of the robot links; τ ∈ R is the input control signal (vector of the control torques of each link); n n R q q C × ∈ ) , ( & is the matrix describing the centrifugal and Coriolis forces; n R q G ∈ ) ( is the vector determining the influence of gravitational forces; n dis R f ∈ is the vector external constantly operating bounded disturbances acting on the manipulator links; S(τ) is the non-linear function of the input signal saturation which describes as follows: