This paper deals with the position and force control for mechanical systems with holonomic constraints. Our concern is the design of a feedback controller such that the closed-loop system has a satisfactory transient response and is less sensitive to various types of disturbances. Using an appropriate transformation, the constrained system is converted into an unconstrained system of lower order. Then, an H∞, control problem involving the reduced system is formulated. In the case of state feedback, a systematic design procedure for solving the problem is presented, where the key step is the solution of an algebraic Riccati equation. An example is given to illustrate the effectiveness of the proposed method.

Issue Section:
Technical Briefs
Topics:
Algebra, Closed loop systems, Control equipment, Design, Feedback, Force control, Position control, State feedback, Transients (Dynamics)
1.
Craig, J. J., 1986, Introduction to Robotics: Machanics and Control, Addison-Wesley, Reading, MA.
2.
Gahinet, P., 1994, “Explicit Controller Formulas for LMI-based H∞ Control,” Proc. Amer. Contr. Conf., Baltimore, pp. 2396–2400.
3.
Khargonekar
P. P.
,
Petersen
I. R.
, and
Zhou
K.
,
1990
, “
Robust Stabilization of Uncertain Linear Systes: Quardratic Stability and H∞ Control Theory
,”
IEEE Transactions on Automatic Control
, Vol.
35
, pp.
356
–
361
.
4.
Krishnan, H., and McClamroch, N. H., 1990, “On Control Systems Described by a Class of Linear Differential-Algebraic Equations: State Realizations and Unear Quadratic Optimal Control,” Proc. American Control Conference, pp. 818–823.
5.
Krishnan
H.
, and
McClamroch
N. H.
,
1992
, “
Computation of State Realization for Control Systems Described by a Class of Linear Differential-Algebraic Equations
,”
Int. J. Control
, Vol.
55
, No.
6
, pp.
1425
–
1441
.
6.
McClamroch
N. H.
,
1990
, “
Feedback Stabilization of Control Systems Described by a Class of Nonlinear Differential-Algebraic Equations
,”
Systems & Control Letters
, Vol.
15
, pp.
53
–
60
.
7.
McClamroch, N. H., 1986, “Singular Systems of Differential Equations as Dynamic Models for Constrained Robot Systems,” Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, pp. 21–28.
8.
Mills
J. K.
, and
Goldenberg
A. A.
,
1989
, “
Force and Position Control of Manipulators During Constrained Motion Tasks
,”
IEEE Transactions on Robotics and Automation
, Vol.
5
, No.
1
, pp.
30
–
46
.
9.
Singh
, et al.,
1985
, “
Singular Value Decomposition for Constrained Dynamics Systems
,”
ASME Journal of Applied Mechanics
, Vol.
52
, pp.
943
–
948
.
10.
Stoorvogel
A. A.
, and
Trentelman
H. L.
,
1990
, “
The Quaratic Matrix Inequality in Singular H∞ Control with State Feedback
,”
SIAM Journal of Control and Optimization
, Vol.
28
, No.
5
, pp.
1190
–
1208
.
11.
Wang
D.
, and
McClamroch
N. H.
,
1993
, “
Position and Force Control for Constrained Manipulator Motion: Lyapunov’s Direct Method
,”
IEEE Transactions on Robotics and Automation
, Vol.
9
, No.
3
, pp.
308
–
313
.
12.
Vukobratovic, K. M., and Potkonjak V., 1982, Dynamica of Manipulator Robots: Theory and Application. Berlin, FRG: Springer-Verlag.
13.
Yu Tie-Jun and Muller, P. C., “Design of Controller for Linear Mechanical Descriptor Systems,” To appear in ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL.
14.
Zhou
K.
,
Khargonekar
P. P.
,
1988
, “
An Algebraic Riccati Equation Approach to H∞ Optimization
,”
Systems & Control Letters
, Vol.
11
, pp.
85
–
91
.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.