Design of given oscillation index scalar controllers: modal and \(H_\infty \)-approaches. (English. Russian original) Zbl 1455.93042
Autom. Remote Control 81, No. 3, 517-527 (2020); translation from Probl. Upr. 2019, No. 2, 2-8 (2019).
Summary: The algorithms of output controllers design are proposed for linear scalar plants, that ensure the desired or attainable values of oscillation index and of degree of stability, determining the settling time. Both modal control and \(H_\infty \)-approach are used in the design procedures. Examples are constructed, demonstrating that striving to provide the degree of stability that is much greater than the distance from the nearest left zero of the plant transfer function to the imaginary axis (even for the minimum phase plants) leads to the quite small gain and phase stability margins, that is unacceptable in practice.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C05 | Linear systems in control theory |
Software:
Robust Control ToolboxReferences:
| [1] | Bode, HW, Network Analysis and Feedback Amplifier Design (1945), New York: Van Nostrand, New York |
| [2] | MacColl, LA, Fundamental Theory of Servomechanisms (1945), New York: Van Nostrand, New York · Zbl 0061.19104 |
| [3] | Hall, AC, The Analysis and Synthesis of Linear Servomechanisms (1943), Cambridge: MIT Press, Cambridge |
| [4] | Solodovnikov, VV, Application of the Method of Logarithmic Frequency Characteristics to the Study of Stability and to the Quality Assessment of Servo and Controlled Systems, Avtomat. Telemekh., 9, 2, 85-103 (1948) |
| [5] | Bessekerskii, VA; Fabrikant, EA, Dinamicheskii sintez system giroskopicheskoi stabilizatsii (1968), Leningrad: Sudostroenie, Leningrad |
| [6] | Bessekerskii, VA; Popov, EP, Teoriya sistem avtomaticheskogo regulirovaniya (1975), Moscow: Nauka, Moscow |
| [7] | Anderson, BDO; Moore, JB, Optimal Control. Linear Quadratic Methods (1989), New York: Prentice Hall, New York |
| [8] | Åström, KJ; Murray, RM, Feedback Systems: An Introduction for Scientists and Engineers (2008), New Jersey: Princeton Univ. Press, New Jersey · Zbl 1144.93001 |
| [9] | Chestnov, VN, Design of Robust H_∞-Controllers of Multivariable Systems Based on the Given Stability Degree, Autom. Remote Control, 68, 3, 557-563 (2007) · Zbl 1126.93333 · doi:10.1134/S0005117907030150 |
| [10] | Horowitz, IM, Synthesis of Feedback Systems (1963), New York: Academic, New York · Zbl 0121.07704 |
| [11] | Aleksandrov, AG, Controller Design in Precision and Speed. I. Minimal Phase One-Dimensional Plants, Autom. Remote Control, 76, 5, 749-761 (2015) · Zbl 1322.93046 · doi:10.1134/S0005117915050021 |
| [12] | Aleksandrov, AG, Design of Controllers by Indices of Precision and Speed. II. Nonminimal-Phase Plants, Autom. Remote Control, 78, 6, 961-973 (2017) · Zbl 1370.93118 · doi:10.1134/S0005117917060017 |
| [13] | Zhou, K.; Doyle, JC; Glover, K., Robust and Optimal Control (1996), New Jersey: Prentice-Hall, New Jersey · Zbl 0999.49500 |
| [14] | Zhou, K.; Doyle, JC, Essentials of Robust Control (1998), New Jersey: Prentice-Hall, New Jersey |
| [15] | Skogestad, S.; Postlethwaite, I., Multivariable Feedback Control. Analysis and Design (2006), New York: Wiley, New York · Zbl 0842.93024 |
| [16] | Anderson, BDO; Moore, JB, Linear Optimal Control (1971), New Jersey: Prentice-Hall, New Jersey · Zbl 0321.49001 |
| [17] | Kwakernaak, H.; Sivan, R., Linear Optimal Control Systems (1972), New York: Wiley, New York · Zbl 0276.93001 |
| [18] | Kwakernaak, H.; Sivan, R., Lineinye optimal’nye sistemy upravleniya (1977), Moscow: Mir, Moscow |
| [19] | Miroshnik, IV, Teoriya avtomaticheskogo upravleniya. Lineinye sistemy (2005), St. Petersburg: Piter, St. Petersburg |
| [20] | Chestnov, VN, Synthesizing H_∞-Controllers for Multidimensional Systems with Given Accuracy and Degree of Stability, Autom. Remote Control, 72, 10, 2161-2175 (2011) · Zbl 1229.93045 · doi:10.1134/S0005117911100134 |
| [21] | Doyle, JC; Francis, BA; Tannenbaum, AR, Feedback Control Theory (1990), New York: Macmillan, New York |
| [22] | Åström, K. J.; Hägglund, T., Advanced PID Control (2006), NC: ISA, NC |
| [23] | Gaiduk, AR, Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (polinomial’nyi podkhod) (2012), Moscow: Fizmatlit, Moscow |
| [24] | Sadomtsev, YV, Solution of the H_∞-Optimization Problems on the Basis of the Principle of Separation, Autom. Remote Control, 73, 1, 56-73 (2012) · Zbl 1307.93145 · doi:10.1134/S0005117912010043 |
| [25] | Doyle, JC; Glover, K.; Khargonekar, PP; Francis, BA, State-space Solution to Standard H_2 and H_∞ Control Problem, IEEE Trans. Autom. Control, 34, 8, 831-846 (1989) · Zbl 0698.93031 · doi:10.1109/9.29425 |
| [26] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequality in System and Control Theory (1994), Philadelphia: SIAM, Philadelphia · Zbl 0816.93004 |
| [27] | Gahinet, P.; Apkarian, P., A Linear Matrix Inequality Approach to H_∞ Control, Int. J. Robust Nonlin, Control, 4, 421-448 (1994) · Zbl 0808.93024 · doi:10.1002/rnc.4590040403 |
| [28] | Balas, GJ; Chiang, RY; Packard, A.; Safonov, MG, Robust Control Toolbox 3. User’s Guide (2010), Natick: The Math Works, Natick |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
