Peter Nachtwey
Member
Z-N was developed back in 1942. It may have been the only option back then but now there are so many better options. The whole idea of increasing the gain to the point of being marginally stable is insane. Another issue is that the results are awful. The response will oscillate and even though the oscillations are supposed to decrease by 1/4 every cycle, there are still too many application where the overshoot that high is unacceptable. Also the settling time is unacceptable. Z-N does not work for many systems.
What Z-N fails to take into account is that there are integrating and non-integrating systems. Temperature and velocity control are non-integrating systems. Tank level control and position control are integrating systems. Systems will also have different types and number of poles. Poles can be real or complex ( imaginary ). Systems with complex poles are more difficult to tune than systems with only real poles. The very difficult systems are those where the open loop system is unstable. Z-N doesn't take any of this into consideration.
Finally, there is no mathematical proof or justification for the Z-N method.
The control guru website shows how to use the IMC ( internal model control ) method. This method works extremely well for non-integrating systems. There is also a mathematical proof or derivation for the controller formulas.
The IMC method is basically using zeros to cancel out all but one pole so the response is like a low pass filter.
Run Beaufort has mention lambda tuning. I think he said he bought a pamphlet on lama tuning years ago for $35. I would have provided Ron the information for free. Lambda tuning is basically a method of placing closed loop poles. This method will work for any system. I call this method pole placement. You can search for 'lambda tuning" or 'pole placement' to get more info. The only real hurdle to using this method is determining the open loop model. For simple applications the step jump method will work and be close enough. I use a method called system identification where I can determine the coefficients for a system of differential equations that is the model. This model will accurately estimate the PV or feedback value given a control signal. I have used this method to find the coefficients for very non-linear systems with many coefficients.
If you starting studying control theory you will come across evaluation methods such as IAE ( integrated absolute error ), ITAE ( integrated time absolute error )
and others. These are methods of find the optimal closed loop pole position. These methods are similar but provide slightly different versions of optimal response.
Then there is linear quadratic control that will also compute controller gains that will place the closed loop poles AND zeros for optimal response. There are some tricks to using LQC that aren't in the books because professors simply copy other peoples work without really understanding.
I know there is going to be a push back because some of this is too complicated. I admit that some of this stuff goes far beyond normal engineering classes but then you must ask yourself. How much is the sloppy control costing?
Today there are much better methods than Z-N
What Z-N fails to take into account is that there are integrating and non-integrating systems. Temperature and velocity control are non-integrating systems. Tank level control and position control are integrating systems. Systems will also have different types and number of poles. Poles can be real or complex ( imaginary ). Systems with complex poles are more difficult to tune than systems with only real poles. The very difficult systems are those where the open loop system is unstable. Z-N doesn't take any of this into consideration.
Finally, there is no mathematical proof or justification for the Z-N method.
The control guru website shows how to use the IMC ( internal model control ) method. This method works extremely well for non-integrating systems. There is also a mathematical proof or derivation for the controller formulas.
The IMC method is basically using zeros to cancel out all but one pole so the response is like a low pass filter.
Run Beaufort has mention lambda tuning. I think he said he bought a pamphlet on lama tuning years ago for $35. I would have provided Ron the information for free. Lambda tuning is basically a method of placing closed loop poles. This method will work for any system. I call this method pole placement. You can search for 'lambda tuning" or 'pole placement' to get more info. The only real hurdle to using this method is determining the open loop model. For simple applications the step jump method will work and be close enough. I use a method called system identification where I can determine the coefficients for a system of differential equations that is the model. This model will accurately estimate the PV or feedback value given a control signal. I have used this method to find the coefficients for very non-linear systems with many coefficients.
If you starting studying control theory you will come across evaluation methods such as IAE ( integrated absolute error ), ITAE ( integrated time absolute error )
and others. These are methods of find the optimal closed loop pole position. These methods are similar but provide slightly different versions of optimal response.
Then there is linear quadratic control that will also compute controller gains that will place the closed loop poles AND zeros for optimal response. There are some tricks to using LQC that aren't in the books because professors simply copy other peoples work without really understanding.
I know there is going to be a push back because some of this is too complicated. I admit that some of this stuff goes far beyond normal engineering classes but then you must ask yourself. How much is the sloppy control costing?
Today there are much better methods than Z-N