PID control algorithms have been used extensively for several process control systems up to now. On the other hand, Clarke has proposed a generalized minimum variance adaptive control system with linear quadratic cost function as self-tuning control method for nonminimum-phase systems. In this paper, we consider the relationship between the PID control system and the generalized minimum variance adaptive control system. Then, it is shown that the PID control system is equivalent to a control strategy of minimizing a cost function in the generalized minimum variance control system. Furthermore, it is shown that PID control system can be regarded as a feedback control system with a pre-compensator. Next, we consider a design method of PID controller based on the generalized minimum variance control theory. Thus, PID gains are determined so as to construct a desired pre-compensator which suppresses an overshoot and shortens settling time or raise time. Finally, we show a numerical simulation result by the present method and apply the method to a pressure control system to show the effectiveness.
Feedback control is inadequate for the fast control of robotic manipulator with low reduction ratios between joints and actuators, since the nonlinearity of manipulator dynamics is by no means negligible. Hierarchical neural network models which account for the generation of motor command of the manipulator whose dynamics are not known, have been proposed recently. In this paper a new method of learning control of manipulator using Sugeno's fuzzy reasoning is proposed, and compared with the ones using neural network models by computer simulations. It is shown that the multi-layered neural network model possesses a great ability to generalize learning, but substantially long period is required for repetitional learning of a short movement pattern. The fuzzy control proposed in this paper does not have enough ability to generalize learning, but is much superior in the speed of learning and does not require the model of the manipulator dynamics.
In this paper, we propose a robust control scheme which achieves trajectory tracking with prescribed accuracy for robot manipulators with bounded unknown parameters. This scheme is based on Lyapunov stability theorem, and the Lyapunov function is constructed using the intertia matrix. Therefore, the control law takes a very simple form which does not include the inverse of the intertia matrix. Moreover, based on the assumption that the dynamic equation can be expressed as a sum of products of unobservable matrices which contain unknown parameters and observable state vectors, this scheme makes the best use of observable states. Due to this we can expect smaller control gains. Finally, the effectiveness of the proposed control sheme is shown by numerical simulations and experimental results using a 2-degree-of-freedom manipulator.