Linearly Combining Sensor Measurements Optimally to Enforce an SPR Transfer Matrix

Caverly, Ryan James; Forbes, James Richard

doi:10.1109/ccta.2018.8511633

Cited by 4 publications

(9 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Figure A, it is shown that all sensor combination methods yield a modified system

\overset{G}{true} false(s false)

that is fairly similar to G ( s ) below 0.3 or 0.4 rad/s. The Bode plots of

\overset{G}{true} false(s false)

in Figure B illustrate that both interior conic sensor combination techniques from Section 3 lead to modified systems that are significantly closer to G d ( s ) for frequencies less than 0.2 rad/s than the SPR sensor combination techniques from the aforementioned work . This is most likely due to the loosened restrictions of allowing

\overset{G}{true} false(s false)

to be interior conic instead of SPR, the lack of matrix equalities in the sensor combination techniques, and the addition of a weighting transfer matrix.…”

Section: Numerical Examplesmentioning

confidence: 89%

“…The increase in the upper conic bound will increase the allowable lower bound on a feedback controller, but this will not have a significant effect. The resulting modified outputs with the

{scriptH}_{2}

‐ and

{scriptH}_{\infty}

‐optimal techniques, respectively, are

\begin{matrix} alignleft \\ align-1 {\bar{y}}_{conic 2} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 1.01 & 0.986 \end{array}] x (t), \\ align-1 {\bar{y}}_{conic \infty} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 1.02 & 0.994 \end{array}] x (t) . \end{matrix}

The

{scriptH}_{2}

‐ and

{scriptH}_{\infty}

‐optimal SPR sensor combination techniques from the work of Caverly and Forbes are also implemented without any weighting transfer matrix, yielding

\begin{matrix} alignleft \\ align-1 {\bar{y}}_{SPR 2} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 0.736 & 0.706 \end{array}] x (t), \\ align-1 {\bar{y}}_{SPR \infty} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 0.925 & 0.887 \end{array}] x (t \end{matrix}

…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The same feedback controller G c ( s ) is also implemented in closed‐loop simulation using the results of the sensor combination techniques from the work of Caverly and Forbes . The chosen controller G c ( s ) is known to also be SPR, as it has the form G c ( s )= k ( s + c )/(( s + a )( s + b )), where

a, b, c \in double-struckR

and 0< c < a + b < ∞…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Combining the full set or a subset of the available sensors allows for greater flexibility in adjusting or prescribing a system's input‐output properties compared to sensor selection, where only subsets of the original open‐loop transfer matrix can be selected. This concept has been used with linear time‐invariant (LTI) systems to optimally combine sensor measurements either in a static linear fashion, with an output compensator, or with an output compensator combined with either a feedback controller or an observer, in such a manner that the new system is positive real (PR) or strictly positive real (SPR). By ensuring the new system is PR/SPR, any SPR/PR negative feedback controller will ensure an asymptotically stable closed‐loop system .…”

Section: Introductionmentioning

confidence: 99%

“…This robustness property is illustrated through numerical examples in Section 6. A preliminary version of the methods presented in this paper appears in the work of Caverly and Forbes, which considers the linear combination of sensor measurements to ensure the new system is SPR and the

{scriptH}_{2}

{scriptH}_{\infty}

norm of the difference between the system with the new combined output and a desired system output is minimized. This paper significantly extends the techniques in the aforementioned work by ensuring the new system is interior conic, considering actuator combination, proposing an iterative sensor and actuator combination method, using weighted

{scriptH}_{2}

{scriptH}_{\infty}

norms, and demonstrating the use of the techniques for robust stabilization.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

Caverly

2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary This paper presents techniques to linearly combine the sensor measurements and/or actuator inputs of a linear time‐invariant system to obtain a new system that is interior conic with prescribed bounds. In the optimal sensor combination problem, a desired system output is defined, and in the optimal actuator combination problem, a desired system input is defined, along with a frequency bandwidth in which the desired system input or output should be matched. The simultaneous optimal sensor and actuator combination problem includes desired system outputs and inputs. In all cases, the weighted scriptH2 or scriptH∞ norm of the difference between the system with linearly combined sensors or actuators and the desired system is minimized while rendering the new system interior conic with prescribed bounds. The weighting transfer matrix used in the scriptH2‐ or scriptH∞‐optimization problem is determined by the frequency bandwidth of interest. The individual sensor and actuator combination methods involve linear matrix inequality constraints and are posed as convex optimization problems, whereas the combined sensor and actuator method is an iterative procedure composed of convex optimization steps. Numerical examples illustrate superior tracking performance with the proposed sensor and actuator combination techniques over comparable techniques in the literature when implemented with a simple feedback controller. Robust asymptotic stability of the closed‐loop system to plant uncertainty is demonstrated in the numerical examples.

show abstract

“…In Figure A, it is shown that all sensor combination methods yield a modified system

\overset{G}{true} false(s false)

that is fairly similar to G ( s ) below 0.3 or 0.4 rad/s. The Bode plots of

\overset{G}{true} false(s false)

\overset{G}{true} false(s false)

to be interior conic instead of SPR, the lack of matrix equalities in the sensor combination techniques, and the addition of a weighting transfer matrix.…”

Section: Numerical Examplesmentioning

confidence: 89%

“…The increase in the upper conic bound will increase the allowable lower bound on a feedback controller, but this will not have a significant effect. The resulting modified outputs with the

{scriptH}_{2}

‐ and

{scriptH}_{\infty}

‐optimal techniques, respectively, are

\begin{matrix} alignleft \\ align-1 {\bar{y}}_{conic 2} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 1.01 & 0.986 \end{array}] x (t), \\ align-1 {\bar{y}}_{conic \infty} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 1.02 & 0.994 \end{array}] x (t) . \end{matrix}

The

{scriptH}_{2}

‐ and

{scriptH}_{\infty}

‐optimal SPR sensor combination techniques from the work of Caverly and Forbes are also implemented without any weighting transfer matrix, yielding

\begin{matrix} alignleft \\ align-1 {\bar{y}}_{SPR 2} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 0.736 & 0.706 \end{array}] x (t), \\ align-1 {\bar{y}}_{SPR \infty} (t) & align-2 = [\begin{array}{cccc} 0 & 0 & 0.925 & 0.887 \end{array}] x (t \end{matrix}

…”

Section: Numerical Examplesmentioning

confidence: 99%

a, b, c \in double-struckR

and 0< c < a + b < ∞…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

{scriptH}_{2}

{scriptH}_{\infty}

{scriptH}_{2}

{scriptH}_{\infty}

norms, and demonstrating the use of the techniques for robust stabilization.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

Caverly

2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

Robust Noncolocated µ-Tip Rate Control of Flexible Robotic Manipulators with Uncertain Dynamics

Halverson,

Kwan Cheah,

Caverly

2023

2023 IEEE Conference on Control Technology and Applications (CCTA)

View full text Add to dashboard Cite

Periodic Tracking Control Using Gain-Scheduled Fourier Series-Based Internal Models

Caverly

Forbes

2019

Volume 3, Rapid Fire Interactive Presentations: Advances in Control Systems; Advances in Robotics and Mechatronics; Automotive

View full text Add to dashboard Cite

This paper presents a gain-scheduled controller composed of a number of positive real controllers that contain internal models of reference command signals. Using the internal model principle as inspiration, and the Passivity Theorem to assure input-output closed-loop stability, the proposed controller is designed to realize tracking while maintaining input-output stability of the closed-loop system. The gain-scheduled nature of the internal models allows for a number of internal models to be simultaneously implemented. In particular, by expressing a periodic reference command as a Fourier series, the first few Fourier modes can be included as internal models in the controllers to be gain-scheduled, which reduces steady-state tracking error. An example involving tracking the outlet temperature of a heat exchanger is presented, where the first nine Fourier modes of the reference signal are used as internal models to reduce tracking error.

show abstract

Linearly Combining Sensor Measurements Optimally to Enforce an SPR Transfer Matrix

Cited by 4 publications

References 23 publications

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

Robust Noncolocated µ-Tip Rate Control of Flexible Robotic Manipulators with Uncertain Dynamics

Periodic Tracking Control Using Gain-Scheduled Fourier Series-Based Internal Models

Contact Info

Product

Resources

About