Multivariable adaptive pid regulatör for manipulator control

Robot arm dynamics deals with the mathematical formulations of the equations of robot arm motion. The dynamic equations of 0>otion of a manipulator are a set of mathematical equations describing the dynamic behavior of the manipulator. Such equations of notion are useful for computer simulation of the robot arm motion, the design of suitable control equations for for a robot arm. The actual dynamic model of a robot arm can be obtained from known physical laws such as the laws of newtonian mechanics and lagrangian mechanics. This leads to the development of the dynamic equations of motion for the various articulated joints of the manipulator in terms of specified geometric and inertial parameters of the links. Conventional approaches like the Lagrange- Euler and Newton-Euler formulations could then be applied systematically to develop the actual robot arm motion equations LSI. The purpose of manipulator control is to maintain the dynamic response of a computer-based manipulator in accordance with sone prespecified system performance and desired goals. In general, the dynamic performance of a manipulator directly depends on the efficiency of the control algorithms and the dynamic model of the manipulator. The control problem consists of obtaining dynamic models of the physical robot arm system and then specifying corresponding control laws or strategies to achieve the desired system response and performance. The basic difficulty in controlling a robot manipulator arises from the fact that the dynamic equations describing the manipulator motion are inherently nonlinear and highly coupled; because of dynamic coupling effects between the joints and varying effective inertias of the links. The complexity of the mathematical model of a manipulator makes the robot control task a difficult and challenging problem.Present day robot manipulators utilize independent joint controllers which control the joint angles separatly through simple position servo loops. This basic control system enables the manipulator to perform simple positioning tasks such as pick -and -place operations. However, it is severely limited in terras of precise tracking of fast trajectories and sustaining desirable dynamic performance for different payloads. The control of robot manipulators has been a very active area of research and two major design categories have emerged. The first category, originated by the classic works of Paul til, Bejczy LB1 and Marki ewics C33, covers robot control techniques based on global linearization of robot dynamics by means of a nonlinear feedback controller. In these tecniques, the nonlinearit ies in the robot robot dynamics ar-e cancelled out by the controller and hence the nonlinear feedback controller is of the same order of complexity as the robot dynamics itself, ftlso in these model-based control tecniques the controller requires knowledge of the full dynamic model and accurate parameter values of the manipulator and the payload. These requirements can be difficult to meet in practice since, for instance, joint friction is difficult to model accurately and is dependent on the operating condition and various adjustments. When perfect cancellations of the robot nonlinearit ies is not achieved due to imperfect modelling or inaccurate parameter values, dynamic performans of the robot may be degraded and a complicated stability analysis is necessitated and this situation may even lead to instability of the closed- loop system. The second category of advanced control systems covers methods based on adaptive control theory and was initiated by the pioneering work of Dubowsky and DesForges C42. The task of the adaptive robot controller is to adjust its gains based on the response of the robot in such a way that the performance of the robot closely matches that of a reference model defined by the designer*. Adaptive control theory is applied on many practical control problems in which we come across: 1. Changes in the plant transfer function, either in its order or in the values of some parameters due to variations in the environment. £. Stochastic disturbances. VI3. uhanges in the nature of inputs. A. Propagation of disturbances along a chain of unit prcesses. 5. Nonlinear behavior. S. Appreciable dead tine. 7. Unknown parameters, as when a control system for a new process is commissioned. In all such situations a conventional controller cannot maintain the performance of the system at acceptable levels. There is, therefore, a need for a special class of control systems which can automatically compensate for these unforeseen variations in parameters and input signals. Early attempts to overcome such problems involved designing an intentionally nonlinear control system with adjustment of, say, the loop gain. Considerable analytical effort is needed to specify the optimum parameter settings. Such a fixed compensator can be succesful over a limeted range of operating conditions. Outside this range the compensation is inadequate and there is degradation of the performance. Practical control systems are usually very complex and their dynamics are not known in detail. The extereme changes in the parameters and/or inputs or random fluctuations occuring within the system are often not measurable. In such situations the control engineer has to employ adaptive control systems which automatically sense and correct themselves whenever drastic disturbances and/or severe changes in the parameters occur. It is also possible to introduce a simple learning mechanism in the adaptive part of the system. Any complexity should be added to the system only if improved performance is mandatory and the costs are justifiable. ftn adaptive control system has to be designed so as to guarantee stability and also robustness in the presence of disturbances. The designer has also to keep in mind the need for high speed of the adaptation algorithm to compensate for parameter variations and the need to use only a small amount of computer time and capacity. One should explore alternative solutions before considering adaptive control. There are situations in VIInoticeably. Thus, the assumption of " slowly tine-varying " robot mode is justified. This mult i variable adaptive PID control algorithm has been applied to a three freedom degree robot. Simulation results arB presented in support of the proposed adaptive control scheme. The results deiEonstrate that the adaptive controller performs remarkably well for different reference trajectories, despite gross variations in the payload, end-effector and measurement errors. The control Scheie has guaranteed convergence in that the actual trajectory qKeyword: Adaptif denetim sistemleri = Adaptive control systems ; Benzetim = Simulation ; Regülator = Regulator ; Robot kolu = Robot arm ; Robotlar = Robots