Briefly describe four kinds of interference observers (1)————Interference observer based on nominal inverse model

There are four types of interference observer series:

1. Disturbance observer based on the nominal inverse model;

2. Disturbance observer based on nonlinear observer;

3. Disturbance observer based on state observer;

4. Disturbance observer based on expanded state in observer.

The observer based on the nominal inverse model uses the robust model matching principle to design the interference compensator. Robust model matching is based on classical control theory, and factors such as interference and uncertainty are considered in the design process. The design goal is to make the transfer function of interference to the output of interest equal to or approximately zero. As shown in the figure below, by observing the output $\tiny y$ and the inverse transfer function of the control object, the external disturbance can be approximated and then introduced into the control system for compensation, theoretically eliminating the influence of the disturbance. In the figure, the $\tiny M\left ( s \right )$ interference observer can be used to estimate the interference. The $\tiny L\left ( s \right )$ term needs to meet a certain function conversion relationship to ensure the correctness of interference compensation. It $\tiny F_{r}\left ( s \right )$ is a filter used to limit the bandwidth of interference suppression.

Simplified system model as follows: where $\tiny W\left ( s \right )$ is the transfer function of the actuator provides torque of the flywheel to herein as an example, the UAV may also refer to the transfer function of the brushless motor, the motor control system may refer to a current loop, generally $\tiny W\left ( s \right )$ can be a Instead of the first-order inertial link, if $\tiny W\left ( s \right )$ the bandwidth is more than five times larger than the bandwidth of the previous loop, it can be considered $\tiny W\left ( s \right )=1$ .

Among them: $\tiny q$ is the generalized disturbance torque including the influence of uncertainty such as flexibility, $\tiny u_{c}$ is the actuator drive command, $\tiny u_{t}$ is the actuator output torque, and $\tiny \dot{\theta }$ is the pitch angular velocity. $\tiny q$ The calculated value (observed value) of generalized interference can be obtained according to the angular velocity output and the controlled object information

$\tiny \hat{q}=I_{y}s\dot{\theta }-u_{t}$ （1）

In order to eliminate the influence of generalized interference, the compensator torque needs $\tiny z_{t}$ to be added on the basis of the corresponding control torque of the controller as

$\tiny z_{t}=-\hat{q}=u_{t}-I_{y}s\dot{\theta }$ （2）

The corresponding execution instructions that need to be added to the actuator $\tiny z_{c}$ can be $\tiny W\left ( s \right )$ obtained by inversely based on the model combined with formula (2)

$\tiny z_{c}=\frac{1}{W_{s}}z_{t}=u_{c}-\frac{I_{y}s}{W_{s}}\dot{\theta }$ （3）

The model of the flywheel actuator $\tiny W\left ( s \right )$ can be simplified to a first-order inertia link

$\tiny W\left ( s \right )=\frac{1}{\tau _{y}s+1}$ （4）

Therefore, it can be seen that the formula (3) has $\tiny u_{c}-I_{y}\ast s\ast \left ( \tau _{y}s+1 \right )\ast \dot{\theta }$ a second-order differential, so the amplifying effect on the noise in the feedback is considerable. If it is directly added to the control system, it will have a very large impact, and the impact of noise must be suppressed. The most commonly used method is to design a low-pass filter to suppress noise. Designing a suitable low-pass filter is the most critical part of the observer. It is necessary to compromise between performance and stability. Ideally, at low frequencies $\tiny F_{r}\left ( s \right )=1$ and high frequencies, $\tiny F_{r}\left ( s \right )=0$ it can be set as a third-order low-pass filter as follows. Refer to Note 2 for the filter design of the complex system.

The filter $\tiny F_{r}\left ( s \right )$ plays a key role in the interference suppression performance of the interference compensator, so it must be designed reasonably. $\tiny F_{r}\left ( s \right )$ Can be selected as

$\tiny F_{r}\left ( s \right )=\frac{\alpha\beta \gamma }{\left ( s+\alpha \right )\left ( s+\beta \right )\left ( s+\gamma \right )}$ （5）

Where: $\tiny \alpha ,\beta ,\gamma$ is the parameter to be designed. As it can be seen $\tiny F_{r}\left ( s \right )$ by in $\tiny \alpha ,\beta ,\gamma$ three low-pass filter cutoff frequency in series, and therefore three or more selected parameters will determine the performance of the interference compensator. $\tiny \alpha ,\beta ,\gamma$ The larger the value, $\tiny F_{r}\left ( s \right )$ the closer to 1; when the $\tiny \alpha ,\beta ,\gamma$ value is smaller, the interference in the desired frequency range cannot be effectively suppressed.

The final model is as follows:

The usual block diagram is represented as the following figure:

Briefly describe four kinds of interference observers (1)————Interference observer based on nominal inverse model

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