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Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Edit on Aug 15th

Someone asked me why I asked this question. It is because of this post actually: https://robotics.stackexchange.com/questions/7853/how-to-tune-pid-for-a-yt-kxt-system

I asked a question on PID controller and there are arguments that the PID controller shall not be followed by an integrator. However, in both real tests and simulation, PID-integrator controller(I only used PI-Integrator) beats pure PID controller. A PI-Integrator Controller is actually an I-II controller with transfer function of \$\dfrac{D}{s} + \dfrac{E}{s^2}\$.

Please correct me if I made any mistake.

Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Someone asked me why I asked this question. It is because of this post actually: https://robotics.stackexchange.com/questions/7853/how-to-tune-pid-for-a-yt-kxt-system

I asked a question on PID controller and there are arguments that the PID controller shall not be followed by an integrator. However, in both real tests and simulation, PID-integrator controller(I only used PI-Integrator) beats pure PID controller. A PI-Integrator Controller is actually an I-II controller with transfer function of \$\dfrac{D}{s} + \dfrac{E}{s^2}\$.

Please correct me if I made any mistake.

Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Edit on Aug 15th

Someone asked me why I asked this question. It is because of this post actually: http://robotics.stackexchange.com/questions/7853/how-to-tune-pid-for-a-yt-kxt-system

I asked a question on PID controller and there are arguments that the PID controller shall not be followed by an integrator. However, in both real tests and simulation, PID-integrator controller(I only used PI-Integrator) beats pure PID controller. A PI-Integrator Controller is actually an I-II controller with transfer function of \$\dfrac{D}{s} + \dfrac{E}{s^2}\$.

Please correct me if I made any mistake.

Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Edit on Aug 15th

Someone asked me why I asked this question. It is because of this post actually: https://robotics.stackexchange.com/questions/7853/how-to-tune-pid-for-a-yt-kxt-system

I asked a question on PID controller and there are arguments that the PID controller shall not be followed by an integrator. However, in both real tests and simulation, PID-integrator controller(I only used PI-Integrator) beats pure PID controller. A PI-Integrator Controller is actually an I-II controller with transfer function of \$\dfrac{D}{s} + \dfrac{E}{s^2}\$.

Please correct me if I made any mistake.

Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Transfer function of a PID controller is: \$I\cdot s + P+\dfrac{D}{s}\$

Are there controllers like: \$A\cdot s^2 + B\cdot s + C+\dfrac{D}{s} + \dfrac{E}{s^2}\$ ?

If so, are they common? Why do people usually just use a PID controller?

Edit on Aug 15th

Someone asked me why I asked this question. It is because of this post actually: http://robotics.stackexchange.com/questions/7853/how-to-tune-pid-for-a-yt-kxt-system

I asked a question on PID controller and there are arguments that the PID controller shall not be followed by an integrator. However, in both real tests and simulation, PID-integrator controller(I only used PI-Integrator) beats pure PID controller. A PI-Integrator Controller is actually an I-II controller with transfer function of \$\dfrac{D}{s} + \dfrac{E}{s^2}\$.

Please correct me if I made any mistake.