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Showing papers by "N.H. McClamroch published in 1990"


Proceedings ArticleDOI
13 May 1990
TL;DR: A feedback control problem for regulation of contact force and position in constrained robot systems is considered and a linear quadratic optimal control problem associated with the linearized differential-algebraic equations is solved.
Abstract: A feedback control problem for regulation of contact force and position in constrained robot systems is considered. The nonlinear differential-algebraic equations which describe the dynamics of a constrained robot system are linearized about a constrained equilibrium. A method of obtaining an equivalent state realization for the resulting linear differential-algebraic equations is developed. This method is numerically efficient since it is based on a singular value decomposition. A linear quadratic optimal control problem associated with the linearized differential-algebraic equations is solved. The resulting linear feedback control law guarantees good regulation of both contact force and position of the constrained robot. Since the method is based on the linearization of the nonlinear differential-algebraic equations, it is valid only in a neighborhood about the point of linearization. Two robot examples are considered in order to illustrate the proposed method. >

39 citations



Proceedings ArticleDOI
05 Dec 1990
TL;DR: In this article, a class of control systems that are represented by equations which are not in the standard singularly perturbed form is studied, and it is shown that the equations for the slow dynamics can be characterized by a set of differential-algebraic equations which can be easily derived from the original equations by setting the parameter to zero.
Abstract: A class of control systems is studied that are represented by equations which are not in the standard singularly perturbed form. Assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form, thereby justifying the two time scale property. It is then possible to show that the equations for the slow dynamics can be characterized by a set of differential-algebraic equations which are easily derived from the original equations by setting the parameter to zero; the original assumptions guarantee the existence of solutions of the obtained differential-algebraic equations. In addition, the equations for the fast dynamics can be expressed in terms of matrices that define the original control system. Control design for the system being considered is studied using the composite control approach. As an example, the problem of contact force and position regulation in a robot with its end effector in contact with a stiff surface is considered. >

9 citations


Journal Article
TL;DR: In this paper, the necessary and sufficient conditions for optimality are transformed into a system of nonlinear algebraic equations in the control switching times during one half of the maneuver, the maneuver time, and the costates at the mid-maneuver time.
Abstract: Attitude controllers for spacecraft have been based on the assumption that the bodies being controlled are rigid. Future spacecraft, however, may be quite flexible. Many applications require spinning up/down these vehicles. In this work the minimum time control of these maneuvers is considered. The time-optimal control is shown to possess an important symmetry property. Taking advantage of this property, the necessary and sufficient conditions for optimality are transformed into a system of nonlinear algebraic equations in the control switching times during one half of the maneuver, the maneuver time, and the costates at the mid-maneuver time. These equations can be solved using a homotopy approach. Control spillover measures are introduced and upper bounds on these measures are obtained. For a special case these upper bounds can be expressed in closed form for an infinite dimensional evaluation model. Rotational stiffening effects are ignored in the optimal control analysis. Based on a heuristic argument a simple condition is given which justifies the omission of these nonlinear effects. This condition is validated by numerical simulation.

2 citations



Proceedings ArticleDOI
13 May 1990
TL;DR: A production system is modeled as a stochastic discrete-event process that produces discrete parts from an infinite supply of raw materials and the optimal operating policy is determined by minimizing the short-term cost function.
Abstract: A production system is modeled as a stochastic discrete-event process. The production system produces discrete parts from an infinite supply of raw materials. The production time for a part is exponentially distributed and can be affected by a control variable-the production rate, which can be adjusted only at production initiation epochs for the discrete parts. A short-term cost criterion is introduced to accommodate two primary economic factors: cost due to the control effort and cost based on missing production deadlines. This short-term cost function depends only on quantities in the production of a single part, but with a correction term to achieve better long-term performance. Two cases are considered in detail: one case where the penalty on missing the part production deadline is asymmetric and another case where the penalty is symmetric. In each case, the optimal operating policy is determined by minimizing the short-term cost function. Properties of the resultant optimal control policy are investigated; the closed-loop behavior of the production system under the optimal control policy is discussed for each case. >