Linear quadratic output tracking and disturbance rejection. (English) Zbl 1245.49048
Summary: This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilizability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard Linear Quadratic Regulation (LQR) problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.
MSC:
| 49N10 | Linear-quadratic optimal control problems |
| 93C73 | Perturbations in control/observation systems |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
linear quadratic regulation (LQR); linear quadratic output tracking; linear quadratic disturbance rejection; optimal trackingReferences:
| [1] | Anderson B, Optimal Control, Linear Quadratic Methods (1989) |
| [2] | DOI: 10.1109/TAC.1985.1103851 · Zbl 0576.93035 · doi:10.1109/TAC.1985.1103851 |
| [3] | DOI: 10.1109/TAC.1987.1104678 · Zbl 0624.93076 · doi:10.1109/TAC.1987.1104678 |
| [4] | DOI: 10.1016/0005-1098(76)90006-6 · Zbl 0344.93028 · doi:10.1016/0005-1098(76)90006-6 |
| [5] | DOI: 10.2307/2296567 · doi:10.2307/2296567 |
| [6] | Huerta F, Bueno, E., Cobreces, S., Rodriguez, F., and Giron, C. (2008) |
| [7] | Kalman R, Bol. Sot. Matem. Mex. 5 pp 102– (1960) |
| [8] | DOI: 10.1080/00207178208932890 · Zbl 0483.93044 · doi:10.1080/00207178208932890 |
| [9] | DOI: 10.1080/002071700219722 · Zbl 1004.93040 · doi:10.1080/002071700219722 |
| [10] | Lin F, Robust Control Design: an Optimal Control Approach (2007) |
| [11] | DOI: 10.1109/TAC.1977.1101470 · Zbl 0356.93016 · doi:10.1109/TAC.1977.1101470 |
| [12] | DOI: 10.1080/00207170802187239 · Zbl 1168.49030 · doi:10.1080/00207170802187239 |
| [13] | DOI: 10.1016/j.sysconle.2004.01.001 · Zbl 1157.49317 · doi:10.1016/j.sysconle.2004.01.001 |
| [14] | DOI: 10.1109/TPEL.2006.880271 · doi:10.1109/TPEL.2006.880271 |
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