This paper deals with the problem of designing a robust controller with an adaptation mechanism in order to reduce conservatism inherent in a robust controller with a fixed gain. It is assumed that the linear state-space model of the plant contains unknown parameters which vary within certain prescribed ranges. To begin with, a parameter-dependent state feedback gain is constructed so as to minimize an upper bound of an appropriately selected quadratic cost function. This design procedure can be reduced to a convex optimization problem. Next, an adaptive law to adjust parameters in the parameter-dependent state feedback gain is presented, by which the adjustable parameters are selected on-line on the boundary surface of the possible parameter space. As a result, asymptotic stability of the proposed control system is ensured. The effectiveness of the proposed method is shown through some simulation results.
This paper proposes a robust high gain adaptive stabilization of minimum phase plants with its relative degree n or n+1. The proposed method uses the fact that any minimum phase plant with its relative degree zero or one can be stabilized by a high gain adaptive control and extends this result by using backstepping. The σ-modification is applied in order to avoid an unnecessarily high gain feedback.
In this paper, we consider a scheduled robust H∞, control problem via state feedback controllers in linear systems with uncertain parameters and scheduling parameters. Controllers are characterized by parameter dependent Linear Matrix Inequalities (LMIs), and a feasible approach to solving parameter dependent LMIs is proposed. A numerical example of fuel diverter and return valve of turbofun engines is discussed.
This paper deals with a tracking control problem for a discrete-time non-minimum phase system in the framework of frequency domain. The contributions are as follows. First, the proposed feedforward controller can provide the overall system with the following frequency characteristics; (i) The phase shift is equal to zero for all frequencies. (ii) The gain at any given frequency is equal to unity. (iii) The maximum deviation of the gain from unity over a given frequency range is less than an arbitrarily given positive number. Especially, the frequency at which the gain is made equal to unity can be chosen arbitrarily, while in the previous schemes, the frequency is restricted to zero. Secondly, the class of desired outputs for which the deadbeat tracking can be achieved is generalized, while in the previous results the class is restricted to only steps and ramps. Thirdly, the proposed controller is given in an explicit form and the design method is simple and straightforward. Finally, an adaptive control system based on the proposed feedforward controller is presented and its effectiveness is demonstrated by simulations.
A piecewise-linear state feedback control law for the systems with constraints, based on the theory of maximal CPI set, is derived. The control law increases the feedback gain in a piecewise constant manner as the controlled error converges toward the origin. It guarantees that input bounds are never exceeded and, as a consequence, maintains stability of the system. The sequence of feedback gains is computed off-line via quadratic and convex optimization techniques. The algorithms for gain switching need on-line computations using observed state variable. These on-line computations are simple, so they can be easily implemented. The proposed switching control law is tested for the inverted pendulum model, and its effectiveness is assured. Possibility of improving the proposed control law by using information of vertices of the maximal CPI set is also discussed. However, this extension requires terrible numerical computations of all vertices of convex polyhedral set. Their subsequent implementation is difficult for higher dimensional plants.
An adaptive servo control system estimating the unknown reference signal model for a single-input single-output plant is proposed. In order to follow reference signals as in servo systems, the models of the reference signals should be included in the control laws as internal models. So far, in the cases that the model of the signals is unknow or varies, a servo control law can not be designed. To design a servo system in such cases, in this paper, an adaptive adjusting law is used to identify the unknown parameters of the reference signal model. To simplify the control system, the design is based on coprime factorization of the plant model over the ring of stable proper rational functions. Stability of the closed-loop system including the proposed adaptive servo system is proved.
This paper presents a design method of adaptive controllers for nonlinear systems with unknown degrees and with uncertain relative degrees. Contrary to the previous researches of adaptive control where the degrees and relative degrees of the controlled objects are assumed to be known exactly, the degrees are assumed to be completely unknown and the relative degrees partly unknown in the present paper. To be exact, the relative degrees are assumed to be r, r+1, or r+2 with known r. It is shown that a single adaptive scheme can deal with such uncertainty of relative degrees and unknown degrees, and that the resulting adaptive systems are asymptotically stable. Several simulation studies also show the effectiveness of the proposed method.
The purpose of this paper is to show the realization of sitting down and standing up motion of a legged robot. In this paper, we present a new design control scheme for the sitting down and standing up motion of our legged robot called Emu. Then we show that the resultant control system has a property of a kind of robustness against some modeling error theoretically. Furthermore, we developed an experimental apparatus named Emu-I that is able to realize the sitting down and standing up motion. Through some experiments, we show the effectiveness of our control scheme.