×

zbMATH — the first resource for mathematics

Integral control by variable sampling based on steady-state data. (English) Zbl 1016.93044
The authors are concerned with the continuous-time, infinite-dimensional \(m\)-input, \(m\)-output system \[ \dot{x}(t)=Ax(t)+Bu(t),\quad x(0)\in X,\qquad y(t)=Cx(t), \] where \(A\) is the generator of an exponentially stable semigroup \(T(t),\) the input operator \(B\) is potentially unbounded, but it is assumed that \(A^{-1}B\) is bounded, and the output operator \(C\) is bounded. A sampled-data integral control approach with fixed integrator gain and convergent adaptive sampling is used. Using the sampling period as a parameter for adaptation, the authors determine appropriate integrator gains based on knowledge of step response data. They investigate robustness of the choice of the integrator gain \(K\) with respect to uncertainty in experimental measurement of the steady-state gain and show how to select the gain robustly. The results are illustrated by a simple two-input, two-output example of a diffusion equation with point actuators and spatially distributed sensors.

MSC:
93C57 Sampled-data control/observation systems
93C25 Control/observation systems in abstract spaces
93C20 Control/observation systems governed by partial differential equations
93C40 Adaptive control/observation systems
93B35 Sensitivity (robustness)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cook, P. A. (1992). Controllers with universal tracking properties. Proceedings of the international IMA conference on control: modelling, computation, information, Manchester.
[2] Davison, E.J., Multivariable tuning regulatorsthe feedforward and robust control of a general servomechanism problem, IEEE transactions on automatic control, 21, 35-47, (1976) · Zbl 0331.93030
[3] Hinrichsen, D.; Pritchard, A.J., Stability radius for structured perturbations and the algebraic Riccati equation, Systems and control letters, 8, 105-113, (1986) · Zbl 0626.93054
[4] Ilchmann, A.; Townley, S., Adaptive sampling control of high-gain stabilizable systems, IEEE transactions on automatic control, 44, 1961-1966, (1999) · Zbl 0956.93056
[5] Logemann, H.; Ryan, E.P., Time-varying and adaptive integral control of infinite-dimensional regular systems with input nonlinearities, SIAM journal of control and optimization, 38, 1940-1961, (2000) · Zbl 0913.93031
[6] Logemann, H.; Ryan, E.P.; Townley, S., Integral control of infinite-dimensional linear systems subject to input saturation, SIAM journal of control and optimization, 36, 1940-1961, (1998) · Zbl 0913.93031
[7] Logemann, H.; Ryan, E.P.; Townley, S., Integral control of linear systems with actuator nonlinearitieslower bounds for the maximal regulating gain, IEEE transactions on automatic control, 44, 1315-1319, (1999) · Zbl 0955.93018
[8] Logemann, H.; Townley, S., Low-gain control of uncertain regular linear systems, SIAM journal of control and optimization, 35, 78-116, (1997) · Zbl 0873.93044
[9] Logemann, H.; Townley, S., Discrete-time low-gain control of uncertain infinite-dimensional systems, IEEE transactions on automatic control, 42, 22-37, (1997) · Zbl 0874.93056
[10] Logemann, H., & Townley, S. (2001). Adaptive low-gain integral control of multivariable well-posed linear systems. SIAM Journal of Control and Optimization, to appear. · Zbl 1043.93035
[11] Lunze, J., Determination of robust multivariable I-controllers by means of experiments and simulation, System analysis modelling simulation, 2, 227-249, (1985) · Zbl 0569.93045
[12] Morari, M., Robust stability of systems with integral control, IEEE transactions on automatic control, 30, 574-577, (1985) · Zbl 0558.93069
[13] Owens, D.H., Adaptive stabilization using a variable sampling rate, International journal of control, 63, 107-119, (1996) · Zbl 0845.93074
[14] Özdemir, N. (2000). Robust and adaptive sampled data I—control. Ph.D. thesis, University of Exeter, UK.
[15] Özdemir, N., & Townley, S. (1998). Adaptive low-gain control of infinite dimensional systems by means of sampling time adaptation. Methods and models in automation and robotics, Miedzyzdroje, Poland (pp. 63-68).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.