Abstract
This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.
| Original language | English |
|---|---|
| Pages (from-to) | 141-149 |
| Number of pages | 9 |
| Journal | International Journal of Control |
| Volume | 72 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jan 1 1999 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
Cite this
Deadbeat control system with time-varying uncertainty : Minimization of worst case steady-state tracking error. / Yamada, Manabu; Riadh, Zaier; Funahashi, Yasuyuki.
In: International Journal of Control, Vol. 72, No. 2, 01.01.1999, p. 141-149.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Deadbeat control system with time-varying uncertainty
T2 - Minimization of worst case steady-state tracking error
AU - Yamada, Manabu
AU - Riadh, Zaier
AU - Funahashi, Yasuyuki
PY - 1999/1/1
Y1 - 1999/1/1
N2 - This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.
AB - This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.
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U2 - 10.1080/002071799221316
DO - 10.1080/002071799221316
M3 - Article
VL - 72
SP - 141
EP - 149
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 2
ER -