digital-brain/content/article/spanos95_soft_activ_vibrat_isolat.md

+++
title = "A soft 6-axis active vibration isolator"
author = ["Thomas Dehaeze"]
draft = false
+++

Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})

Reference
: ([Spanos, Rahman, and Blackwood 1995](#orgad76892))

Author(s)
: Spanos, J., Rahman, Z., & Blackwood, G.

Year
: 1995

**Stewart Platform** (Figure [1](#org6d10ec2)):

-   Voice Coil
-   Flexible joints (cross-blades)
-   Force Sensors
-   Cubic Configuration

<a id="org6d10ec2"></a>

{{< figure src="/ox-hugo/spanos95_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}

Total mass of the paylaod: 30kg
Center of gravity is 9cm above the geometry center of the mount (cube's center?).

Limitation of the **Decentralized Force Feedback**:

-   high frequency pole due to internal resonances of the struts
-   low frequency zero due to the rotational stiffness of the flexible joints

After redesign of the struts:

-   high frequency pole at 4.7kHz
-   low frequency zero at 2.6Hz but non-minimum phase (not explained).
    Small viscous damping material in the cross blade flexures made the zero minimum phase again.

<a id="orgfef5d56"></a>

{{< figure src="/ox-hugo/spanos95_iff_plant.png" caption="Figure 2: Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage" >}}

The controller used consisted of:

-   second order low pass filter to gain stabilize the plant at high frequencies and provide steep roll-off
-   first order lead filter to provide adequate phase margin at the high frequency crossover
-   first order lag filter to provide adequate phase margin at the low frequency crossover
-   a first order high pass filter to attenuate the excess gain resulting from the low frequency zero

The results in terms of transmissibility are shown in Figure [3](#orgec62915).

<a id="orgec62915"></a>

{{< figure src="/ox-hugo/spanos95_results.png" caption="Figure 3: Experimentally measured Frobenius norm of the 6-axis transmissibility" >}}


## Bibliography {#bibliography}

<a id="orgad76892"></a>Spanos, J., Z. Rahman, and G. Blackwood. 1995. “A Soft 6-Axis Active Vibration Isolator.” In _Proceedings of 1995 American Control Conference - ACC’95_, nil. <https://doi.org/10.1109/acc.1995.529280>.
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
+								+++
 								title = "A soft 6-axis active vibration isolator"
 								author = ["Thomas Dehaeze"]
 								draft = false
 								+++
 								Tags
 								: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
 								Reference
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								: ([Spanos, Rahman, and Blackwood 1995](#orgad76892))
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
 								Author(s)
 								: Spanos, J., Rahman, Z., & Blackwood, G.
 								Year
 								: 1995
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								**Stewart Platform** (Figure [1](#org6d10ec2)):
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
 								-   Voice Coil
 								-   Flexible joints (cross-blades)
 								-   Force Sensors
 								-   Cubic Configuration
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								<a id="org6d10ec2"></a>
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
 								{{< figure src="/ox-hugo/spanos95_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
 								Total mass of the paylaod: 30kg
 								Center of gravity is 9cm above the geometry center of the mount (cube's center?).
 								Limitation of the **Decentralized Force Feedback**:
 								-   high frequency pole due to internal resonances of the struts
 								-   low frequency zero due to the rotational stiffness of the flexible joints
 								After redesign of the struts:
 								-   high frequency pole at 4.7kHz
 								-   low frequency zero at 2.6Hz but non-minimum phase (not explained).
 								    Small viscous damping material in the cross blade flexures made the zero minimum phase again.
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								<a id="orgfef5d56"></a>
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
 								{{< figure src="/ox-hugo/spanos95_iff_plant.png" caption="Figure 2: Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage" >}}
 								The controller used consisted of:
 								-   second order low pass filter to gain stabilize the plant at high frequencies and provide steep roll-off
 								-   first order lead filter to provide adequate phase margin at the high frequency crossover
 								-   first order lag filter to provide adequate phase margin at the low frequency crossover
 								-   a first order high pass filter to attenuate the excess gain resulting from the low frequency zero
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								The results in terms of transmissibility are shown in Figure [3](#orgec62915).
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
+								<a id="orgec62915"></a>
-												Add content folder

											
										
										
											2020-04-20 18:58:10 +02:00
 								{{< figure src="/ox-hugo/spanos95_results.png" caption="Figure 3: Experimentally measured Frobenius norm of the 6-axis transmissibility" >}}
-												Update all files with new citeproc-org package

											
										
										
											2020-08-17 23:00:20 +02:00
 								## Bibliography {#bibliography}
 								<a id="orgad76892"></a>Spanos, J., Z. Rahman, and G. Blackwood. 1995. “A Soft 6-Axis Active Vibration Isolator.” In _Proceedings of 1995 American Control Conference - ACC’95_, nil. <https://doi.org/10.1109/acc.1995.529280>.