In this paper, we present a synthesis method for global stability and performance of input constrained linear plants. We consider the multi-stage anti-windup scheme that uses two sets of static anti-windup gains. Unlike traditional two-step anti-windup design procedures, our method synthesizes all controller parameters simultaneously. This simultaneous design also provides an opportunity to guarantee different levels of performance based on the magnitude of the controller output. The synthesis results are cast as an optimization over linear matrix inequalities. The benefits of the proposed method are illustrated with a well-known example.
BoydSEl GhaouiLFeronE. (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM.
2.
BurgatCTarbouriechS (1998) Intelligent anti-windup for systems with input magnitude saturation. International Journal of Robust and Nonlinear Control8: 1085–1100.
3.
DaiDHuTSTeelAR. (2009) Output feedback design for saturated linear plants using deadzone loops. Automatica45: 2917–2924.
4.
de SouzaCELiX (1999) Delay-dependent robust H∞ control of uncertain linear state-delayed systems. Automatica35: 1313–1321.
5.
DoALGomes da SilvaJMSenameO. (2011) Control design for LPV systems with input saturation and state constraints: an application to a semi-active suspension. Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, pp. 3416–3421.
6.
EdwardsCPostlethwaiteI (1998) Anti-windup and bumpless-transfer schemes. Automatica34: 199–210.
7.
GaleaniSTarbouriechSTurnerMCZaccarianL (2009) A tutorial on modern anti-windup design. European Journal of Control3: 418–440.
8.
Gomes da SilvaJMLimonDAlamoT. (2008) Dynamic output feedback for discrete-time systems under amplitude and rate actuator constraints. IEEE Transactions on Automatic Control53: 2367–2372.
9.
GrimmGHatfieldJPostlethwaiteI. (2003) Antiwindup for stable linear systems with input saturation: an LMI-based synthesis. IEEE Transactions on Automatic Control48: 1509–1525.
10.
MulderEFKothareMVMorariM (2001) Multivariable anti-windup controller synthesis using linear matrix inequalities. Automatica37: 1407–1416.
11.
MulderEFTiwariPYKothareVK (2009) Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization. Automatica45: 805–811.
12.
Sajjadi-KiaSJabbariF (2009) Modified anti-windup compensators for stable plants. IEEE Transactions on Automatic Control54: 1934–1939.
13.
Sajjadi-KiaSJabbariF (2010) Scheduled static anti-windup augmentation synthesis for open-loop stable plants. Proceedings of American Control Conference, MD, pp. 6751–6756.
14.
Sajjadi-KiaSJabbariF (2011) Multi-stage anti-windup compensation for open-loop stable plants. IEEE Transactions on Automatic Control56: 2166–2172.
15.
Sajjadi-KiaSJabbariF (2012) Modified dynamic anti-windup through deferral of activation. International Journal of Robust and Nonlinear Control22: 1661–1673.
16.
SawadaKKiymaTIwasakiT (2009) Generalized sector synthesis of output feedback control with anti-windup structure. Systems and Control Letters58: 421–428.
17.
SchererCGahinetPChilaliM (1997) Multiobjective output-feedback control via LMI optimization. IEEE Transactions on Automatic Control42: 896–911.
18.
TarbouriechSTurnerMC (2009) Anti-windup design: an overview of some recent advances and open problems. IET Control Theory and Applications3: 1–19.
19.
WuFGrigoriadisKMPackardA (2000) Anti-windup controller design using linear parameter-varying control methods. International Journal of Control73: 1104–1114.
20.
WuXJLinZL (2012) Design of multiple anti-windup loops for multiple activations. Science China-Information Sciences55: 1925–1934.
21.
YuJWangLXieG (2010) Disturbance rejection of switched systems subject to actuator saturation. Transactions of the Institute of Measurement and Control32: 603–634.
22.
ZhangMChenFWangY (2013) State-feedback design for input-saturating quadratic systems with disturbance attenuation. Transactions of the Institute of Measurement and Control36: 147–154.
