Multi-stage Control Design of Strictly Positive Real H2 Controllers

This paper presents a robust control design using strictly positive realness for second-order dynamic systems. A robust strictly positive real controller stabilizes second-order systems with only acceleration measurements. An important property of this design is that the stabilization is independent of the system plant parameters. The control design connects a virtual system to a given plant such that any strictly positive real controller can be used to achieve robust stability. A spring-mass system is used as an example to demonstrate the robust stability and robust performance of this design.

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New Results on the Characterization of Strictly Positive Real Matrix Transfer Functions

IEEE Transactions on Automatic Control ◽

10.1109/tac.2020.2980936 ◽

2021 ◽

Vol 66 (1) ◽

pp. 335-339

Author(s):

Mojtaba Hakimi-Moghaddam ◽

Augusto Ferrante

Keyword(s):

Transfer Functions ◽

Real Matrix ◽

Positive Real ◽

Strictly Positive Real

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Active Helmholtz Resonator With Positive Real Impedance

Journal of Vibration and Acoustics ◽

10.1115/1.2345678 ◽

2006 ◽

Vol 129 (1) ◽

pp. 94-100 ◽

Cited By ~ 5

Author(s):

Jing Yuan

Keyword(s):

Noise Control ◽

Helmholtz Resonator ◽

Control Device ◽

Positive Real ◽

Noise Field ◽

Strictly Positive Real ◽

Control Devices ◽

Passive Noise ◽

Active Resonator ◽

Electronic Resonance

The impedance of a passive noise control device is strictly positive real, if the device is installed in noise fields with weak mean flows. Passive noise control devices are, therefore, more reliable than active ones. Active control may be applied to a Helmholtz resonator to introduce electronic resonance. It will affect the impedance Zact of the resonator. A controller may be designed such that (a) Zact is small and resistive at some tunable frequencies; and (b) Re{Zact}⩾0 in the entire frequency range of interest. If criterion (a) is satisfied, the active resonator can suppress duct noise at tunable frequencies. It is difficult to design a controller to satisfy criterion (b) because parameters of the controller depend on acoustic parameters of the noise field. A new method is proposed here to design an active controller to meet both criteria simultaneously. The satisfaction of criterion (b) implies a positive real Zact and a robust active resonator with respect to parameter variation in the noise field. Experimental results are presented to verify the performance of the active resonator.

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On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

Mathematical Problems in Engineering ◽

10.1155/2018/7861396 ◽

2018 ◽

Vol 2018 ◽

pp. 1-17

Author(s):

M. De la Sen

Keyword(s):

Continuous Time ◽

Linear Time ◽

Positive Real ◽

Feedback Controllers ◽

Linear Time Invariant ◽

Continuous Time Systems ◽

Strictly Positive Real ◽

Forward Transfer ◽

Time Invariant ◽

Time Systems

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

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