## Dissertations

#### Title

Two dimensional agonistic control

Dissertation

Fall 1-31-1997

#### Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)

#### Department

Electrical and Computer Engineering

Bernard Friedland

Andrew Ulrich Meyer

Timothy Nam Chang

John Tavantzis

Anthony P. Tzes

#### Abstract

The conventional method of precise multiple-axis motion control entails use of a multiple axis positioning system with each axis carrying not only the workpiece but also the positioning system of the remaining axes. The resultant structure is heavy, sluggish, and expensive. An alternative positioning technique is being investigated in which the motion of the workpiece is controlled by pulling it with tendons, each of which has its own actuator. Since the actuators can be mounted on the base of the structure instead of being carried by motion system of the other axes, they can be relatively large and powerful without the need for a massive structure such as is found in a conventional motion control system. This method of control is given the appellation agonistic, based on the usages of the word suggesting tension or a contest.

Agonistic control system can be used for low cost accurate positioning of workpiece. The control task can be moving the workpiece from one point to another point and kept there or tracking a given trajectory. While the workpiece moves, the tendons should be always kept in tension.

In this thesis, the model of two dimensional agonistic control (in the case of tendons of infinite elastic modulus) is established. It leads to a nonlinear multi-variable control problem. Based on this nonlinear model, a full-state feedback control law is synthesized. It is composed of two parts. The first part is a feedforward control to cancel the nonlinear dynamics. The second part is a PD control term which requires velocity information. In the practice, velocity measurement may be contaminated by noise. In order of only using position measurement in the control law, a nonlinear observer is designed to provide the velocity information.

Numerical simulation is performed to verify the ability of the proposed control law.

In reality, the tendon has some elasticity. This finite elasticity, if not accounted for, can render the closed-loop system unstable. The investigation shows that the effect of elastic tendons can be compensated for by appropriately modifying the control law designed for inelastic tendons. In particular, the control law is synthesized using the singular perturbation method. It consists of a fast control and a slow control. The fast control is used to stablize the oscillations incurred by the finite elasticity of the tendon. The slow control drives the system to track the desired trajectory. Robustness of the controller is enhanced by using sliding mode control.

In the chapter 4, the design of observer in the elastic case is addressed. Linear uncertain system theory is used. The observer is globally stable.

The use of decentralized control scheme makes very simple the controller design and reduces the computational complexity. It is very useful for real time agonistic control. A design approach is presented for the decentralized control scheme. A simple linear second order model is used instead of complex nonlinear model used in centralized version. In this approach, the tension in each tendon is treated as disturbance, estimated by an observer, to be compensated.

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