Optimization of automatic control system parameters

Laboratory work No.7 on the course "Control in technical systems"

Purpose of the work

  • Familiarization with the optimization procedures in SimInTech on the example of the synthesis of the optimal integral controller

Formulation of tasks for parametric optimization of ACS

To get acquainted with the basic optimization procedures in SimInTech, it is necessary to use the block diagram from laboratory work No.1, which is presented in Figure (Figure 1).


Figure 1. Block diagram of ACS.
The control object is presented as a block Oscillatory block labeled "W2(s)" with the following property values:
  • "Gain factor" = "1"
  • "Time constant" = "1"
  • "Damping factor" = "0.5"
Local feedback is presented as a block Aperiodic block of the 1st order labeled "W3(s)" with the following property values:
  • "Gain factor" = "0.6"
  • "Time constant" = "5"
It is necessary to determine the parameter "Gain factor" in the block Integratorto form ACS that meets the following criteria:
  • when applying a step disturbance, there is no overshoot
  • setting time does not exceed 20 s

When performing laboratory work No.1, the direct modeling method was used, which made it possible to determine the value of the controller gain equal to "0.35" in just three attempts, in which the transient in the ACS simultaneously satisfied both of the above limitations.

If there is no recommendations for varying speed gain values, the search for the optimal value could be difficult. With an increase in the number of variable parameters, the search strategy by the selection method becomes not obvious.

SimInTech implements a block Optimizer, which allows to perform an automated search for such values of the variable parameters of the ACS, in which the dynamic characteristics of the ACS (and the transient process, in particular) meet the optimality criteria.

Sequence of actions for optimization

The list of main steps to be performed to implement optimization:
  • Set variable parameters as global variables (more precisely, the project signal) using the appropriate interface procedures
  • Form local optimization criteria that are necessary to solve the main optimization problem
  • Put the block on the diagram Optimizer and enter the required data in its settings, including:
    • names of variable parameters, their range limits and simulation error
    • names of local criteria and permissible limits of their values
    • calculation method of optimization and its settings
  • Start simulation

Setting the variable parameter as a global project signal

To set global signals, click the button in the menuService and select an itemSignals (Figure 2), then a window will open List of project signals.


Figure 2. Item "Signals".
There is also a separate button in the main SimInTech window (Figure 3) for quick access to project signals.


Figure 3. "Signals" button.

The project signal list allows you to create a list of variables that are used in the simulation process and provide access to these variables by their name.

In the window List of project signals click button Add signal to add a new signal with the possibility of changing its parameters.

To optimize the test task, you need to create three signals:
  • “k1" – gain factor - parameter that is optimized in the task
  • "tpp" – setting time
  • "dy" – overshoot value
Create three signals and adjust their parameters according to Figure (Figure 4).


Figure 4. List of project signals.

The variables of this list can be used as properties of the blocks of the simulation diagram.

In the properties of the block labeled "W1(s)", set the variable "k1" (Figure 5) instead of the numeric value in the numerator and denominator.


Figure 5. Properties of the block labeled "W1(s)".

Simulation of local optimization criteria

To simulate the parameters of the transient process, a submodel is used, in which a computational scheme will be created.

Put the block on the diagram Submodel from tab Substructures and enter the submodel. To the workspace of the block Submodel place two blocks Input port. It is recommended to place them on the left side one under the other, then their order will correspond to the order of the inputs of the block to schematic of the upper level.

To the workspace of the block Submodel the following blocks should be placed:
  • 1 block Absolute value from tab
  • 1 block Clock from tab Sources
  • 1 block Key-3 from tab Keys
  • 1 block Delay on the integration step from tab Nonlinear
  • 1 block Lower or upper limit from tab Nonlinear
  • 2 blocks Output port from tab Substructures
  • 2 blocks Recording to the list of signals from tab Signals
Form a block diagram and put labels for the blocks according to Figure (Figure 6).


Figure 6. Simulation of the parameters of the transient.
To configure the simulation of the parameters of the transient, you should set the values of the submodel blocks:
  • In the properties of the block labeled "Tolerance value" (Key-3) in the "Setpoint values" line, enter a value equal to "0.04", which corresponds to a 5% tolerance for the future steady state value
  • In the block properties Lower or upper limitset "Operation type" – "Maximum". This block will record the maximum value of the value received from the input port in the signal list
  • Double-click on the blocks Input port to open window Submodel port and in the "Submodel port names" field, set the port names "Error" and "y(t)" in accordance with Figure (Figure 6)
  • In the block properties Recording to the list of signals set the "Signal names"property to "tpp" and "dy" according to Figure (Figure 6)
The setting time simulation diagram works as follows:
  • To the middle (logical) input port of the block Key-3 (tolerance value), the absolute value of the error is supplied
  • If this signal is greater than the setpoint (5% of 0.8), then to the block output Key-3a signal is transmitted from the third (lower) input port, i.e. the current model time
  • If the control signal (at the middle input port) is less than the setpoint, then to the block outputKey-3 a signal is transmitted from the first (upper) input port, i.e. the same signal, but delayed by one integration step
  • The delay on the integration step is carried out by a block labeled "Setting time" (block Delay on the integration step from tabNonlinear)

Thus, after the simulation is completed, the variables "tpp" and "dy" will contain the value of the setting time and the maximum value of the output from the block with the label "W2(s)".

Exit the submodel workspace by double-clicking on the free space of the project window or by clicking the button Back from submodel.

Connect the signal lines according to Figure (Figure 7).


Figure 7. Diagram with the simulation of the parameters of the transient.

Setting up the "Optimizer" block

Put the following blocks on the diagram:
  • 2 blocks Reading from signal list from tab Signals
  • 1 block Recording to the list of signals from tab Signals
  • 1 block Multiplexer from tab Vector
  • 1 block Optimizer from tab Analysis and optimization
Form a block diagram and put labels for the blocks according to Figure (Figure 8).


Figure 8. Block diagram with "Optimizer" block.

Configure the blocks Reading from signal list and Recording to the list of signals according to Figure (Figure 8).

Description of the schematic operation: two signals, the maximum value – "dy", and the setting time – "tpp", calculated in the block Submodel, are packed in a vector and transmitted to the block Optimizer, this block calculates the value transmitted to the signal "k1", which, in turn, determines the property "Gain factor" in the block with the label "W1(s)", and must provide the specified characteristic of the transient process.

As optimization parameters, we use the setting time and the maximum value during the transient process, respectively, optimization should be calculated for the entire transient process.

Block Optimizer can simulate optimal values also during the transient, but for this it is necessary to use the optimization criteria calculated at each time point.

Set block properties Optimizer according to Figure (Figure 9)


Figure 9. "Optimizer" block properties.

Simulation of the optimal controller

By clicking the button Start simulation is started in the main window. It should be noted that with the added optimization block in the "Over the full transient" mode, the model in SimInTech is calculated not once in dynamics, but several times until the optimal result is obtained. In this case, information about the optimized parameter and the reached optimization criteria appears in the message window, at the bottom of the schematic window.

At the end of the simulation, the transient plot will take the form according to Figure (Figure 10).


Figure 10. Plot of the optimized transient.
To view the value of the signal "k1", in which the optimized value of the coefficient is recorded, you need to double-click on the block labeled "W1(s)" or open List of project signals (Figure 11).


Figure 11. Properties of the block labeled "W1(s)".

Conclusion

The demonstration and introductory task is completed. The project must be saved.