**Appendix A. Equations of Used Filters and Switches**

This section includes the continuous functions of the used filters and switches. All filters are given in the Laplace domain. The equivalent form for discrete time can be found in [16]. The first order low-pass filtered value of a general variable is given by:

$$\mathbf{x}\_{LP}(\mathbf{s}) = \frac{1}{\boldsymbol{\pi} \cdot \mathbf{s} + 1} \cdot \mathbf{x}(\mathbf{s}),\tag{A1}$$

where *τ* is the filter time constant.

The second order low-pass filter of a general signal takes the form

$$\chi\_{LP}(s) = \frac{\omega^2}{s^2 + 2\xi\omega \cdot s + \omega^2} \cdot x(s). \tag{A2}$$

Here *x* and *xLP* denote the original and low-passed signal respectively. *ω* is the filter frequency and *ξ* the damping factor.

A band pass filter of a general variable is implemented as:

$$\mathbf{x}\_{BPF}(\mathbf{s}) = \frac{2\mathbf{j}^x\_\mathbf{s}\omega \cdot \left(\mathbf{s} + \mathbf{r}\cdot\mathbf{s}^2\right)}{\mathbf{s}^2 + 2\mathbf{j}^x\_\mathbf{s}\omega \cdot \mathbf{s} + \omega^2} \cdot \mathbf{x}(\mathbf{s}),\tag{A3}$$

where *ω* is the center frequency, *ξ* the damping ratio and *τ* a time constant.

The notch filter of a general signal takes the form

$$\mathbf{x}\_{NF}(\mathbf{s}) = \frac{\mathbf{s}^2 + 2\mathbf{J}\_p^\chi \boldsymbol{\omega} \cdot \mathbf{s} + \boldsymbol{\omega}^2}{\mathbf{s}^2 + 2\mathbf{J}\_1 \boldsymbol{\omega} \cdot \mathbf{s} + \boldsymbol{\omega}^2} \cdot \mathbf{x}(\mathbf{s}),\tag{A4}$$

where *ξ*<sup>1</sup> and *ξ*<sup>2</sup> are the damping ratios and *ω* the filter frequency.

The general form of the switching function used by the controller is given by the equation

$$\sigma(\mathbf{x}\_0, \mathbf{x}\_1, \mathbf{x}) = \begin{cases} 0 & \text{for } \mathbf{x} < \mathbf{x}\_0 \\ a\_3 \mathbf{x}^3 + a\_2 \mathbf{x}^2 + a\_1 \mathbf{x} + a\_0 & \text{for } \mathbf{x}\_0 \le \mathbf{x} < \mathbf{x}\_1 \\ 1 & \text{for } \mathbf{x} \ge \mathbf{x}\_1 \end{cases} \tag{A5}$$

where the coefficients take following values:

$$\begin{aligned} a\_3 &= \frac{2}{(\mathbf{x}\_0 - \mathbf{x}\_1)^3} \\ a\_2 &= \frac{-3(\mathbf{x}\_0 + \mathbf{x}\_1)}{(\mathbf{x}\_0 - \mathbf{x}\_1)^3} \\ a\_1 &= \frac{6\mathbf{x}\_0\mathbf{x}\_1}{(\mathbf{x}\_0 - \mathbf{x}\_1)^3} \\ a\_0 &= \frac{(\mathbf{x}\_0 - 3\mathbf{x}\_1)\mathbf{x}\_0^2}{(\mathbf{x}\_0 - \mathbf{x}\_1)^3} .\end{aligned} \tag{A6}$$

#### **Appendix B. Abbreviations**

Table A1 lists the abbreviations used in this work.

**Table A1.** Abbreviations used in this work.

