Update Content - 2021-09-03
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: [Decentralized Control](decentralized_control.md), [Multivariable Control](multivariable_control.md)
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Reference
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: ([Albertos and Antonio 2004](#orgea6b25f))
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: ([Albertos and Antonio 2004](#org9f7e5c2))
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Author(s)
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: Albertos, P., & Antonio, S.
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@ -76,10 +76,10 @@ This strategy is called **decoupling**.
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### Feedforward Decoupling {#feedforward-decoupling}
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A pre-compensator (Figure [1](#orgaa5070b)) can be added to transform the open-loop characteristics into a new one as chosen by the designer.
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A pre-compensator (Figure [1](#org92f4052)) can be added to transform the open-loop characteristics into a new one as chosen by the designer.
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This decoupler can be taken as the inverse of the plant provided it does not include RHP-zeros.
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{{< figure src="/ox-hugo/albertos04_pre_compensator_decoupling.png" caption="Figure 1: Decoupler pre-compensator" >}}
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@ -109,10 +109,10 @@ where \\(U\\) and \\(V\\) are orthogonal matrices and \\(\Sigma\\) is diagonal.
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The SVD can be used to obtain decoupled equations between linear combinations of sensors and linear combinations of actuators.
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In this way, although losing part of its intuitive sense, a decoupled design can be carried out even for non-square plants.
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If sensors are multiplied by \\(U^T\\) and control actions multiplied by \\(V\\), as in Figure [2](#orge470e39), then the loop, in the transformed variables, is decoupled, so a diagonal controller \\(K\_D\\) can be used.
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If sensors are multiplied by \\(U^T\\) and control actions multiplied by \\(V\\), as in Figure [2](#org9e1f260), then the loop, in the transformed variables, is decoupled, so a diagonal controller \\(K\_D\\) can be used.
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Usually, the sensor and actuator transformations are obtained using the DC gain, or a real approximation of \\(G(j\omega)\\), where \\(\omega\\) is around the desired closed-loop bandwidth.
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{{< figure src="/ox-hugo/albertos04_svd_decoupling.png" caption="Figure 2: SVD decoupling: \\(K\_D\\) is a diagonal controller designed for \\(\Sigma\\)" >}}
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@ -187,4 +187,4 @@ The solution is similar to that of the wind-up phenomenon: the regulator should
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## Bibliography {#bibliography}
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<a id="orgea6b25f"></a>Albertos, P., and S. Antonio. 2004. “Decentralized and Decoupled Control.” In _Multivariable Control Systems: An Engineering Approach_, 125–62. Advanced Textbooks in Control and Signal Processing. Springer-Verlag. <https://doi.org/10.1007/b97506>.
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<a id="org9f7e5c2"></a>Albertos, P., and S. Antonio. 2004. “Decentralized and Decoupled Control.” In _Multivariable Control Systems: An Engineering Approach_, 125–62. Advanced Textbooks in Control and Signal Processing. Springer-Verlag. <https://doi.org/10.1007/b97506>.
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