ali8
Member level 2
I am reading "[Small Unmanned Aircraft: Theory and Practice]" (page 7). We have the following Transfer Function (TF):
\[\phi(s)=\frac{a_{\phi 2}}{s(s+a_{\phi 1})}(\delta_a(s)+\frac{1}{a_{\phi 2}}d_{\phi 2})\]
where \[\delta_a\] is the output signal to the actuator and \[d_{\phi 2}(s)\] is an unwanted disturbance.
Initially, the disturbance is neglected, and only a PD controller is employed, and the resulting 2nd order TF (with \[k_p\] and \[k_d\])is compared with the general second-order TF:
\[H(s)=\frac{\omega_n^2}{s^2+2\zeta \omega_ns+\omega_n^2}\]
From which the value of \[k_d\] is obtained (and \[k_p=\frac{\delta_{a,max}}{e_{max}}\], where \[e_{max}\] is the maximum error).
Then, the disturbance is considered, and an integrator is added to get a full PID. The resulting TF (with \[k_p\],\[k_d\] and \[k_i\]) will be different, actually it will become 3rd order. However, the book does not update the values of the gains after the integrator has been added, and somehow claims that the integrator will basically nullify the disturbance, so no change is needed for the gains.
Can anyone explain this to me?
\[\phi(s)=\frac{a_{\phi 2}}{s(s+a_{\phi 1})}(\delta_a(s)+\frac{1}{a_{\phi 2}}d_{\phi 2})\]
where \[\delta_a\] is the output signal to the actuator and \[d_{\phi 2}(s)\] is an unwanted disturbance.
Initially, the disturbance is neglected, and only a PD controller is employed, and the resulting 2nd order TF (with \[k_p\] and \[k_d\])is compared with the general second-order TF:
\[H(s)=\frac{\omega_n^2}{s^2+2\zeta \omega_ns+\omega_n^2}\]
From which the value of \[k_d\] is obtained (and \[k_p=\frac{\delta_{a,max}}{e_{max}}\], where \[e_{max}\] is the maximum error).
Then, the disturbance is considered, and an integrator is added to get a full PID. The resulting TF (with \[k_p\],\[k_d\] and \[k_i\]) will be different, actually it will become 3rd order. However, the book does not update the values of the gains after the integrator has been added, and somehow claims that the integrator will basically nullify the disturbance, so no change is needed for the gains.
Can anyone explain this to me?
