Tuning PID Controllers: Is the Devil as Scary as He is Painted? Part 2. Double-circuit system. Control System Tuner

When implementing an object position control system, a two-loop structure is often used, which includes two regulators: the load position and the speed of the actuator. In this case, it becomes necessary to simultaneously adjust both regulators. This task can be solved using the tool Control System Tuner…

System model

The block diagram of the two-loop system and its model, created on the basis of this diagram, are shown below.

The parameters of the drive and the load are indicated in the first part of the series.

The difference between Electric actuator and Load models is the addition of new sensors: the angular speed sensor measures the rotor speed of the actuator motor and the position sensor measures the position of the controlled object.

We will use P and PI controllers as position and speed controllers, respectively, the latter having a ± 24 V output signal limitation, and it implements the clamping method to combat integral saturation.

The input signal for the system is the required angle of rotation of the load, which should vary within the range of ± 60 °.

Without regulators, i.e. assuming $W_ {p_ {i}} (s) = 1$ , the transient process is aperiodic with the transient process time equal to 2.5 s.

We will present the following requirements for the system transient process:

Overshoot no more than 5%;
Transient time (Settling time) less than 1 s.

Setting up controllers

The Control System Tuner application is located in the tab APPS Simulink model windows, under CONTROL SYSTEMS…

The regulators are tuned in accordance with the following algorithm:

After opening the application window, go to the tab TUNING and press the button Select block…
In the opened dialog box, click on the button Add Blocks to add controller blocks.
Check the box next to the required blocks and confirm the selection by pressing the button OK… As a result, the selected blocks will be displayed in the section Tuned blocks panels Data Browser…
We create a new task for configuration. To do this, press the button New goal and in the drop-down menu select the option Tracking of step commands in section TIME-DOMAIN REQUIREMENTS… This will open the Step Tracking Goal dialog box.
System input and output signals must be specified. For this in the fields
Specify step-response inputs and Specify step-response inputs push the button
Add signal to list → Select signal from model…

Go to the model window and select the corresponding signals, in our case Reference and Position. Returns to the application window. The Select Signals dialog should display the selected signal. Click on the button Add Signal (s)…
Set the desired type of transient on the panel Desired response and, accordingly, the form of the transfer function of the process. You can choose between First-order characteristics, Second-order characteristics, or another type of process (Custom reference model). For our case, we choose an oscillatory process.
In field Time constant the time constant is indicated ( $inline$ ) of the process transfer function in seconds. In the Overshoot (%) field – the amount of overshoot ( $inline$ ). The relationship between the time constant of the oscillating link and the time of the transient ( $, t_ {p.p.} ,$ ) and damping coefficient ( $inline$ ) and overshoot are expressed by the dependencies [1]:

$T = frac {4 t_ {p.p.}} { zeta},$

$zeta = - frac {ln , sigma} { sqrt { pi ^ 2 + ln ^ {2} , sigma}}$

Thus, the maximum value of the time constant that meets the requirement is 0.1725 s. We indicate a time constant equal to 0.1 s. We also enter the required overshoot value in the second field. We confirm the changes.
In the appeared graphic window of the application, you can see two transients: the current one, i.e. transient process of the system before adjusting the regulators, and the desired one, according to a given transfer function. Click on the button Tune for adjusting the regulators. Selecting custom blocks on the panel Data Browser in section Data Preview you can view the view of the transfer function of the controller and the selected parameters. When you select the current configuration task in the section Tuning Goals system input and output signals as well as the process transfer function are displayed. The characteristics of the transient are shown below. It can be seen that these values correspond to the required ones.
To automatically update controller parameters, go to the tab CONTROL SYSTEM and press the button Update Blocks…