Robust PI and PID controller design in delta domain

This note presents a control design method for determining proportional-integral-type controllers satisfying specifications on gain margin, phase margin, and an upper bound on the (complementary) sensitivity for a finite set of plants. The approach can be applied to plants that are stable or unstable, plants given by a model or measured data, and plants of any order, including plants with delays. The algorithm is efficient and fast, and as such can be used in near real-time to determine controller parameters (for online modification of the plant model including its uncertainty and/or the specifications). The method gives an optimal controller for a practical definition of optimality. Furthermore, it enables the graphical portrayal of design tradeoffs in a single plot, highlighting the effects of the gain margin, complementary sensitivity bound, low frequency sensitivity and high frequency sensor noise amplification.Index Terms-Design, gain and phase margin, linear systems, proportional-integral (PI) control, robustness.

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“…such that (6) is an equality. Moreover, since at that particular !, (6) is minimum, its derivative (with respect to !) at the same !…”

Section: Resultsmentioning

confidence: 99%

“…Crowe and Johnson [5] presented an automatic PI control design algorithm to satisfy gain and phase margin based on a converging algorithm. Suchomoski [6] developed a tuning method for PI and PID controllers that can shape the nominal stability, transient performance, and control signal to meet gain and phase margins.…”

Section: Introductionmentioning

confidence: 99%

Robust pi controller design satisfying sensitivity and uncertainty specifications

Yaniv

Nagurka

2003

IEEE Trans. Automat. Contr.

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“…In [4], a design method of nonlinear robust controller is presented for power system by back-stepping method. In [5], a design method of robust PI and PID controller is presented in frequency domain. In [6], robust optimal controller is proposed for nonlinear system via Hamilton-Jacobi-Bellman solution.…”

Section: Introductionmentioning

confidence: 99%

Study on robust stability inverse problem for linear systems

Huang

Zeng

et al. 2014

2014 CACS International Automatic Control Conference (CACS 2014)

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most of traditional robust problems focus on developing a robust controller to stabilize the dynamic system when system parameters perturb in certain bounded range. However, this paper studies the robust inverse problem, that is to say studying robust stability's inverse problem (RSIP) for linear systems. In other words, it needs to find at least a stable system parameters' perturbation space (SSPPS) for any given stable controller. A robust stability's inverse theorem is proposed for linear systems, and SSPPS of stable controllers can be determined by inverse theorem. SSPPS is investigated by inverse theorem when system parameters appear perturbations. Numerical example and results are shown correctness and effectiveness of robust stability's inverse theorem.

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“…However, the concept of time-scale presented herein is such that, when the particular case of discrete-time systems is considered, the description of the dynamics relies on the difference operator, in opposition to the more conventional models based on the shift operator [3]- [5]. A description of a dynamical system based on the difference operator is often referred to as delta-domain description [6]- [12]. When signals are sampled at a high sampling rate the delta-domain models are less sensitive to round-off errors and do not yield ill-conditioned models, as often happens with models based on the shift-operators [13]- [15].…”

Section: Introductionmentioning

confidence: 99%

Transfer Equivalence and Realization of Nonlinear Input-Output Delta-Differential Equations on Homogeneous Time Scales

Casagrande

Kotta

Tõnso

et al. 2010

IEEE Trans. Automat. Contr.

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Fig. 4. Constraint variables z (dotted), v (dashed), and v (solid) for the upper constraint of the uncertain active magnetic bearing system for the initial condition x(0) = [0:5; 0; 0] and the safety control law.while this would clearly happen without the invariance control. In Fig. 4 the time trajectories of the three constraints z 1;1 ; v 1;1 ; v 1;2 are shown. All three constraints are kept below zero at all times, hence the overall constraint is satisfied. The constraint v1;2 (solid line) would be the first to become positive, which is avoided by the invariance controller. VI. CONCLUSIONIn this paper, an algorithm is proposed to construct control laws for uncertain nonlinear systems under hard state constraints. Using a recursive design procedure, a set of safe initial conditions is constructed that can be rendered invariant by a suitable control action. A switching control is designed to guarantee positive invariance of the set and to satisfy a nominal control objective whenever possible. With some additional assumptions, stability of the closed loop is established.The current work focuses primarily on single input systems. However simulations show that a generalization to multiinput systems is possible. An important problem that remains open is with regards to the simultaneous satisfaction of state and input constraints. The backstepping approach seems to offer the flexibility to integrate both challenges into the controller design. Future research will aim to provide a sound theoretical analysis of this problem. ACKNOWLEDGMENTThe authors wish to thank the anonymous reviewers, who helped to improve the paper significantly. REFERENCES[1] M. Bürger and M. Guay, "Robust constraint satisfaction for continuous-time nonlinear systems," in Proc. 47th Conf.[8] P. Tsiotras and M. Arcak, "Low-bias control of amb subject to voltage saturation: State-feedback and observer designs," IEEE Trans.Abstract-Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a state-space realization of a nonlinear input-output delta-differential equation.

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Robust PI and PID controller design in delta domain

Cited by 16 publications

References 13 publications

Robust pi controller design satisfying sensitivity and uncertainty specifications

Robust pi controller design satisfying sensitivity and uncertainty specifications

Study on robust stability inverse problem for linear systems

Transfer Equivalence and Realization of Nonlinear Input-Output Delta-Differential Equations on Homogeneous Time Scales

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