.
diff --git a/content/inbook/levine11_contr_system_applic.md b/content/inbook/levine11_contr_system_applic.md
new file mode 100644
index 0000000..8358e78
--- /dev/null
+++ b/content/inbook/levine11_contr_system_applic.md
@@ -0,0 +1,236 @@
++++
+title = "Advanced Motion Control Design"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+:
+
+
+Reference
+: ([Levine 2011](#orgb7728f4)), chapter 27
+
+Author(s)
+: Levine, W. S.
+
+Year
+: 2011
+
+
+## Introduction {#introduction}
+
+The industrial state of the art control of motion systems can be summarized as follows.
+Most systems, by design, are either decoupled, or can be decoupled using static input-output transformations.
+Hence, most motion systems and their motion software architecture use SISO control design methods and solutions.
+
+Feedback design is mostly done in the frequency domain, using [Loop-Shaping](loop_shaping.md) techniques.
+A typical motion controller has a PID structure, with a low pass at high frequencies and one or two notch filters to compensate flexible dynamics.
+In addition to the feedback controller, a feedforward controller is applied with acceleration, velocity from the reference signal.
+
+The setpoint itself is a result of a setpoint generator with jerk limitation profiles (see [Trajectory Generation](trajectory_generation.md)).
+If the requirements increase, the dynamic coupling between the various DOFs can no longer be neglected and more advanced MIMO control is required.
+
+
+
+
+Centralized control
+: the transfer function matrix of the controller is allowed to have any structure
+
+Decentralized control
+: diagonal controller transfer function, but constant decoupling manipulations of inputs and outputs are allowed
+
+Independent decentralized control
+: a single loop is designed without taking into account the effect of earlier or later designed loops
+
+Sequential decentralized control
+: a single loop is designed with taking into account the effect of all earlier closed loops
+
+
+
+
+For that reason, the step-by-step approach is proposed:
+
+1. Interaction Analysis
+2. Decoupling Transformations
+3. Independent SISO design
+4. Sequential SISO design
+5. Norm-based MIMO design
+
+
+
+
+ The frequency dependent relative gain array is calculated as:
+
+ \begin{equation}
+ \text{RGA}(G(j\omega)) = G(j\omega) \times (G(j\omega)^{-1})^{T}
+ \end{equation}
+
+ where \\(\times\\) denotes element wise multiplication.
+
+
+
+
+ The structured singular value interaction measure is the following condition:
+
+ \begin{equation}
+ \mu\_D(E\_T(j\omega)) < \frac{1}{2}, \forall \omega
+ \end{equation}
+
+ with \\(E\_T(j\omega) = G\_{nd}(j\omega) G\_d^{-1}(j\omega)\\), \\(\mu\_D\\) is the structured singular value, with respect to the diagonal structure of the feedback controller.
+ \\(G\_d(s)\\) are the diagonal terms of the transfer function matrix, and \\(G\_{nd}(s) = G(s) - G\_d(s)\\).
+
+ If a diagonal transfer function matrix is used, controllers gains must be small at frequencies where this condition is not met.
+
+
+
+
+Then the MIMO closed-loop stability assessment can be slit up in two assessments:
+
+- the first for stability of N non-interacting loops, namely \\(\det(I + G\_d(s)K(s))\\)
+- the second for stability of \\(\det(I + E\_T(s)T\_d(s))\\)
+
+
+
+
+Centralized control
+: the transfer function matrix of the controller is allowed to have any structure
+
+Decentralized control
+: diagonal controller transfer function, but constant decoupling manipulations of inputs and outputs are allowed
+
+Independent decentralized control
+: a single loop is designed without taking into account the effect of earlier or later designed loops
+
+Sequential decentralized control
+: a single loop is designed with taking into account the effect of all earlier closed loops
+
+
+
+
+For that reason, the step-by-step approach is proposed:
+
+1. Interaction Analysis
+2. Decoupling Transformations
+3. Independent SISO design
+4. Sequential SISO design
+5. Norm-based MIMO design
+
+
+
+
+ The frequency dependent relative gain array is calculated as:
+
+ \begin{equation}
+ \text{RGA}(G(j\omega)) = G(j\omega) \times (G(j\omega)^{-1})^{T}
+ \end{equation}
+
+ where \\(\times\\) denotes element wise multiplication.
+
+
+
+
+ The structured singular value interaction measure is the following condition:
+
+ \begin{equation}
+ \mu\_D(E\_T(j\omega)) < \frac{1}{2}, \forall \omega
+ \end{equation}
+
+ with \\(E\_T(j\omega) = G\_{nd}(j\omega) G\_d^{-1}(j\omega)\\), \\(\mu\_D\\) is the structured singular value, with respect to the diagonal structure of the feedback controller.
+ \\(G\_d(s)\\) are the diagonal terms of the transfer function matrix, and \\(G\_{nd}(s) = G(s) - G\_d(s)\\).
+
+ If a diagonal transfer function matrix is used, controllers gains must be small at frequencies where this condition is not met.
+
+
+
+
+Then the MIMO closed-loop stability assessment can be slit up in two assessments:
+
+- the first for stability of N non-interacting loops, namely \\(\det(I + G\_d(s)K(s))\\)
+- the second for stability of \\(\det(I + E\_T(s)T\_d(s))\\)
+
+