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Proceedings of the 3rd Workshop on Control Mechanics in Honor of the 65th Birthday of George Leitmann January 22–24, 1990, University of Southern California
Almost all industrial robots exhibit joint flexibility due to mechanical compliance of their gear boxes. In this paper we outline the design of three controllers for flexible joint robots. Two of the three controllers are suitable for parameter adaptation, the candidate Lyapunov functions for these two controllers are derived from arm energy considerations. The desired actuator trajectory in...
The results of efforts to extend the Direct Principle of Lyapunov to stability analysis in controlled output space are described. The motivation is to apply the DPL in the space of the actual variables of concern in the system performance, thus avoiding conservatism and in some cases gaining other advantages. The details of the application of the procedure are developed, and an example is presented.
In the framework of stochastic mechanics, the following problem is considered : in a set of admissible feedback controls v, with range in En, find one minimizing the expectation ESX{∝ST L(t,ξ(t), v(t,ξ(t)))dt+WT(ξ(T))} for all (s,x) ∈ [0,T)⊗En, where L(t,x,v) = (1/2)mv2-U(t,x) is the classical action integrand and ξ is a n-dimensional diffusion process (in the weak sense [17])...
We consider a general food-chain system subject to uncertain disturbances. A Liapunov design methodology is used to establish control growth policies of qualitative nature aimed to restrict the fluctuations of the size of the chain elements (populations, consumers, resources), hence to facilitate transition from growth (decay) to manageable population levels.
The problem of stabilizing a class of linear uncertain systems by using linear state feedback is addressed. The system possesses uncertainty which is time-varying, unknown, but lies within a prescribed bounded set. No statistical information of the uncertainty is imposed. Nor any matching condition is required. Necessary and sufficient conditions for quadratic stabilizability are formulated. The controller...
A class of linear singularly perturbed systems with singular perturbation parameter μ>0 is considered. To assure asymptotic stability of the full order system for μ>0 sufficiently small, it is customary to require that both the reduced-order system (μ=0) and the boundary layer system are asymptotically stable. Here we relax the requirement on the boundary layer system to stability (i.e., not...
Trajectory control of robotic manipulators is investigated using a robust linear control law. For a system with unknown but bounded parameters, we implement an inverse dynamics control scheme that consists of a feedback linearizing control (inner loop) based on a nominal system, followed by a robust linear feedback control (outer loop) based on the uncertainty bounds. The control is robust in the...
We consider n-DOF manipulator arm with untruncated nonlinearity (Coriolis forces, nonreduced coupling) subject to bounded uncertainty in inertia, payload and gravity. The latter is compensated adaptively by varying the feedback controller, whose objective is to track a generally nonlinear reference model. The classical linear MRAC technique is augmented to serve the case concerned, under the condition...
The most widely-used guidance law for short range homing missiles is Proportional Navigation (Pro. Nav.). In Pro. Nav. the acceleration command is proportional to the line of sight angular velocity (L.O.S rate). Indeed, if a missile and a target move on collision course with constant speeds the L.O.S rate is zero. The speed of a highly maneuverable modern missile varies cnsiderably during flight...
This paper presents a sufficient condition for the existence of a symmetric positive definite solution of a Riccati equation that appears in the design of a practically stabilizing controller for mismatched uncertain dynamical systems. It is used to compare two existing methods for stabilizing mismatched systems; one that involves measure of mismatch and the other that uses the Riccati equation. The...
In this paper, the complete derivation of the vector-channel-lattice filter algorithm for least-squares estimation of an input/output model based on the delta operator is presented. Algorithms for residual errors and the auto regressive coefficients are presented also.
The object of this paper is the estimation of stability boundaries and regions of asymptotic stability with sliding for a class of relay-control systems. The direct method of Lyapunov is used to obtain these estimates. A coordinate transformation which brings the system into a special canonical form is utilized to facilitate the stability analysis. The proposed approach to stability regions estimation...
The problem of residence time control by the observer based output feedback is formulated and solved for the case of linear systems with small additive input noise. Both noiseless and noisy measurements are considered. In the noiseless measurements case, it is shown that the fundamental bounds on the achievable residence time depend on the nonminimum phase zeros of the system. In the noisy measurements...
Aircraft densities in terminal areas increase each year, and the risk of collision grows proportionally. The maintenance of clearance between aircraft in this environment sometimes calls for evasive maneuvers, which depend on the relative position and relative velocity of two aircraft. Small amplitude maneuvers are found for both aircraft in near-miss configurations with short time-to-go. Using low-order...
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