Automation Systems
Lecture 9 - Tuning of the controller
Jakub Mozaryn
Institute of Automatic Control and Robotics, Department of Mechatronics, WUT
Warszawa, 2016
Selection of controllers
The basic premise when choosing the type of controller is dynamic characteristics of the controlled process.
Rysunek:Control system
Basic equations, describing the properties of the controlled processes
Gob(s) = ∆ym(s)
∆u(s) = kob
T s + 1e−T0s, Gob(s) = ∆ym(s)
∆u(s) = 1 T se−T0s
Selection of controllers
for T0
Tz
< 0, 1 ÷ 0, 2 → switch controllers (two- three- gain),
for 0, 1 ¬ T0
Tz
< 0, 7 ÷ 1 ÷ 0, 2 → continuous controllers,
dla T0
Tz
> 1 → impulse controllers (impulse output signals)
In the case of industrial processes common ratio of T0
Tz is in the range of 0, 2 ÷ 0, 7. Therefore, in industrial control systems the most common controllers are continuous, with typical control algorithms P, PI, PD and PID.
Selection of controllers
Analysis of controler action with the process leads to the following conclusions concerning the selection of the control algorithm:
PI algorithm provides good control only for the low frequencies of setpoint changes or disturbancs. Integral action is necessary to obtain zero error in steady state.
PI algorithm provides wider bandwidth than PID algorithm, but poorer performance for the low frequencies of setpoint changes or disturbancs.
Derivative action is recommended for objects with higher order lag (such as thermal processes), because it allows the strong interaction of control even at small deviations. PD controller does not ensure the achievement of zero deviation in steady-state . PID algorithm merges to a certain extent the advantages of PI and PD algrithms.
Selection of controllers
In practice, industrial controllers with continuous algorithm and perfor- mance are commonly used. Their parameters (settings) can be changed (adjusted) within a wide range, so they can work properly with processes with different dynamical properties.
Depending on the requirements of the stability and quality, the controller settings are selected by the special selection procedures.
There are following settings of PID controller:
proportional gain kp= 0, 1 ÷ 100 integral gain Ti = 0, 1 ÷ 3600s derrivative gain Td = 0 ÷ 3600s
Selection of controllers
Methods of PID controllers tuning:
Experimental methods - do not allow to achieve certain quality of the control system, eg. Ziegler – Nichols, Pessen, Hassen and Offereissen, Cohen-Coon, ¨Astr¨om – Hagglund .
Tabular methods - determining the set of controller parameters based on the parameters of a mathematical model of the controlled process and the required quality criterion of the control system (like the lowest overshoot, short settling time, problem: often
minimization of different quality index base on the contrary requirements).
Autotuning, eg. relay method.
Tuning of the controllers
Ziegler-Nichols method
Type 1:
controller settings are selected on the basis of the parameters of the closed loop control system, brought to the border of stability (by experimental excitation of the system).
It can be used to controller tuning in the control systems where processes are described by static and astatic, higher order lag elements.
Type 2:
It can be used to controller tuning in the control systems where processes are described by static higher order lag elements, controller settings are selected based on the transient response of the controlled process.
Ziegler-Nichols method, type 1
Rysunek:Functional scheme of real control system
Ziegler-Nichols method, type 1 - steps 1-3 / 6
Step 1: In the manual mode (M) by changing control variable (CV), adjust the process variable ym (PV) to a state in which it is equal with the required setpoint
Step 2: Set the controller to the proportional action (switch off integral and derivative actions), set the operation point control value of the controller equal to the setting obtained in the Step 1 and set the initial value of the controller gain kp> 0.
Step 3: Switch the system to automatic control (A) and if the system maintains equilibrium, by changing SP produce an impulse with some amplitude and pulse duration depending on the expected dynamics of the process; observe or record the change in the controlled variable. It is recommended to use a pulse with amplitude of 10 % of the process value changes ym(PV) and pulse duration of about 10 % of the estimated value of the time constant of the controlled process.
Ziegler-Nichols method, type 1 - steps 4-5 / 6
Step 4: If the transient response is underdamped, set higher values of the proportional gain (Steps 1-3) until a system be on the border of stability (constant oscillations).
Step 5: From the steady oscillations read ’critical’ proportional gain kpkryt.and oscillation period Tosc.
Step 6: Set the patameters according to the table of setings developed by Ziegler-Nichols.
Rysunek:Changes of the process variable (PV) obtained during Ziegler –
Ziegler-Nichols method, type 1
PID controller setting according to Ziegler-Nichols
Controller tyoe kp Ti Td
P 0, 50kpkryt. - -
PI 0, 45kpkryt. 0, 8Tosc • PID 0, 60kpkryt. 0, 5Tosc 0, 12Tosc
Automation Systems
Lecture 9 - Tuning of the controller
Jakub Mozaryn
Institute of Automatic Control and Robotics, Department of Mechatronics, WUT
Warszawa, 2016
