Feedback Controller

For this control system, the output variable is the pitch rate, $q$. The reference signal $q_{\mathrm cmd}$ comes directly from the pilot's control stick. The control is $\delta_e$, the elevator deflection.

We now invent a new abstract control, namely $\dot q_{\mathrm cmd}$. This is the commanded angular acceleration, and the feedback controller will treat it as the control variable. Once the controller has determined $\dot q_{\mathrm cmd}$, the control mixer will choose $\delta_e$ to yield the desired $\dot q$, using Equations 1-3.

The controller design was modeled after the pitch-rate control augmentation system from Reference [2], except that the $\alpha$ feedback loop is not present. Figure 1 presents the block diagram for the control system.

Figure 1: Block diagram of control system for this report

The values of the gains are $K_p=-25$ and $K_I=-1$, which I admit I found mostly by trial and error. These values give good performance. Figure 2 shows the performance of the control system using the known aircraft model (i.e., not the estimated parameters). Figure 2 shows $q$ and $q_{\mathrm cmd}$ for a pull-up maneuver (note that $q$ is negative for a pull-up), and we see that $q$ follows $q_{\mathrm cmd}$ quite well, with only about a 0.1 second lag.

Figure 2: Commanded and actual pitch rates for a pull-up maneuver, while not using parameter identification.