Buck Converter Model

Buck converters convert DC to DC. This model uses a switching power supply to convert a 30V DC supply into a regulated DC supply. The converter is modeled using MOSFETs rather than ideal switches to ensure that device on-resistances are correctly represented. The converter response from reference voltage to measured voltage includes the MOSFET switches. PID design requires a linear model of the system from the reference voltage to the measured voltage. However, because of the switches, automated linearization results in a zero system. In this example, usingPID Tuner, you identify a linear model of the system using simulation instead of linearization.

For more information on creating a buck converter model, seeBuck Converter(Simscape Electrical).

open_system('scdbuckconverter') sim('scdbuckconverter')

The model is configured with a reference voltage that switches from 15 to 25 Volts at 0.004 seconds and a load current that is active from 0.0025 to 0.005 seconds. The controller is initialized with default gains and results in overshoot and slow settling time.

open_system('scdbuckconverter/Scope 1') open_system('scdbuckconverter/Scope 2')

Simulate Model to Generate I/O Data

To open the PID Tuner, in theFeedback controllersubsystem, open thePID Controllerblock dialog, and clickTune.PID Tunerindicates that the model cannot be linearized and returned a zero system.

PID Tuner提供了几个选择when linearization fails. In thePlantdrop-down list, you can select one of the following methods:

For this example, clickIdentify New Plantto open the Plant Identification tool. For plant identification, you must specify a finite value for the Simulink model stop time.

To open a tool that simulates the model to collect data for plant identification, on the植物鉴别tab, clickGet I/O Data > Simulate Data.

On theSimulate I/O Datatab, you simulate the plant seen by the controller. The software temporarily:

This data describes the response of the plant seen by the controller. ThePID Tuneruses this response data to estimate a linear plant model.

Configure the input signal as a step input with the following properties:

SelectShow Input Response,Show Offset Response, andShow Identification Data. Then, click theRun Simulation. The植物鉴别plot is updated.

The red curve is the offset response. The offset response is the plant response to a constant input of. The response shows that the model has some transients with a constant input, in particular:

The blue curve shows the complete plant response that contains the contributions from the initial transients (significant for times < 0.001 seconds), the response to the cyclic current load (time durations 0.0025 to 0.005 seconds), reference voltage change (at 0.004 seconds), and response to the step test signal (applied at time 0.003 seconds). In contrast, the red curve is the response to only the initial transients, reference voltage step, and cyclic current load.

The green curve is the data that will be used for plant identification. This curve is the change in response due to the step test signal, which is the difference between the blue (input response) and red (offset response) curves taking into account the negative feedback sign.

To use the measured data to identify a plant model, clickApply. Then, to return to plant identification, clickClose.

植物鉴别

PID Tuner标识一个工厂使用生成的数据模型by simulating the model. You tune the identified plant parameters so that the identified plant response, when provided the measured input, matches the measured output.

You can manually adjust the estimated model. Click and drag the plant curve and pole location (X) to adjust the identified plant response so that it matches the identification data as closely as possible.

To tune the identified plant using automated identification, clickAuto Estimate. The automated tuning response is not much better than the interactive tuning. The identified plant and identification data do not match well. Change the plant structure to get a better match.

To designate the identified model as the current plant for controller tuning, ClickApply.PID Tunerthen automatically tunes a controller for the identified plant and updates theReference Trackingstep plot.

Controller Tuning

The PID Tuner automatically tunes a PID controller for the identified plant. The tuned controller response has about 5% overshoot and a settling time of around 0.0006 seconds. Click theReference Trackingstep plot to make it the current figure.

The controller output is the duty cycle for the PWM system and must be limited to [0.01 0.95]. To confirm that the controller output satisfies these bounds, create a controller effort plot. On thePID Tunertab, in theAdd Plotdrop-down list, underStep, clickController effort. Move the newly createdController effortplot to the second plot group.

In theController effortplot, the tuned response (solid line) shows a large control effort required at the start of the simulation. To achieve a settling time of about 0.0004 seconds and overshoot of 9%, adjust theResponse TimeandTransient Behaviorsliders. These adjustments reduce the maximum control effort to the acceptable range.

To update the Simulink block with the tuned controller values, clickUpdate Block.

To confirm the PID controller performance, simulate the Simulink model.

bdclose('scdbuckconverter')