1© 2016 The MathWorks, Inc.

Accelerating Control System Design

Using Systematic Approach

Naga Pemmaraju

Senior Application Engineer,

Modeling & Controls

Jayaraj Lakshmanan

Senior Training Engineer,

Modeling & Controls

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What is a Control System?

A control system is a device, or set of devices, that manages, commands,

directs or regulates the behavior of other devices or systems.

Source: Wikipedia

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System

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Controller Plant

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What is a Control System?

A control system is a device, or set of devices, that manages, commands,

directs or regulates the behavior of other devices or systems.

Source: Wikipedia

Plant

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Controller

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s3

System

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What is a Control System?

A control system is a device, or set of devices, that manages, commands,

directs or regulates the behavior of other devices or systems.

Source: Wikipedia

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System

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s1 s2

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Objectives in Control System Design

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System

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Controller Plant

Stability

Transient and Steady State Behavior

Robustness

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Systematic Approach of Designing a Control System

Plant Modeling

(including Linearization)

Analyze(understand current state of system)

Design the Controller

Closed Loop Simulation

Iterate

Real Time Testing &

Deployment

Latent Pain

Time to Design

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Accelerating Control System Design Using Systematic Approach

Plant Modeling

(including Linearization)

Analyze(understand current state of system)

Design the Controller

Closed Loop Simulation

Iterate

Real Time Testing &

Deployment

• Linearization of Plant

• Automatic PID Controller

Tuning

• Multi-Loop Controller

Tuning

• Response Optimization

• Gain Scheduling

• Model Predictive Control

AGENDA

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MATLAB and Simulink Help Land

Unpiloted Boeing Spacecraft

ChallengeDesign a guidance, navigation, and control (GN&C) system

that allows the X-40A to land and come to a full stop on a

standard runway without either power or a pilot

SolutionUse MathWorks tools to streamline software implementation,

shorten the design-to-software-to-verification cycle, and enable

them to make late changes

Results Rapid development within budget

A successful test flight

A contract to continue development

"I am very pleased with the

results of this flight test.

It is a significant step in the

development phase."

John Fuller

Boeing

Boeing X-40A – in test flight (directly above)

and on the ground (top).

Link to user story

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SimulinkA Platform for Model Based Design

• Dynamic Systems Modeling and Simulation

• Design of Controller and Filters

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Introduction to Simulink

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Example: Mass-Spring-Damper

y

u

k b

m

m

𝑘(𝑢 − 𝑦) 𝑏 𝑢 − 𝑦

System Schematic Free Body Diagram Transfer Function

𝑚 𝑦 𝑡 = 𝑘 𝑢 𝑡 − 𝑦 𝑡 + 𝑏 )𝑢(𝑡 − )𝑦(𝑡

𝑌 𝑆

)𝑈(𝑆=

𝑏𝑠 + 𝑘

𝑚𝑠2 + 𝑏𝑠 + 𝑘

System Analysis

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System Analysis- Time Domain

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System Analysis - Frequency Domain

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Linearization

Linearization is a 2 step process

– Finding operating point

– Obtaining the Linear Model

Different Ways of Linearization

– Operating point based

Trimming

Snap shot

– Frequency response estimation

Use Simulink Control Design and the Control System Toolbox to

automatically linearize the plant, design and tune your PID controllers

Linear Analysis Tool

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LinearizationFrequency Response Estimation

Computation of a model’s

frequency response from a

graphical tool

Easy specification of input signal

Optional initialization of input signal

from the exact linearization results

Plotting of frequency response

together with exact linearization results

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Automatic PID tuning

Use Simulink Control Design and the Control System Toolbox to

automatically linearize the plant, design and tune your PID controllers

reference+

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controller

S1 S2

S3

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PID Tuner App

Automatically finds the

design that balances

performance and robustness

Lets you easily try different

controller structures

Provides two sliders for fine-

tuning the design

Several response plots can

be displayed simultaneously

Interactive tuning of PID

controllers

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Gain Scheduled PID Controllers

• Common strategy for

controlling systems

whose dynamics change

with time or operating

condition.

• Well suited for Linear

parameter-varying (LPV)

systems and large

classes of nonlinear

systems

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Control design and linearizationMulti-input, multi-output control tuning

• SYSTUNE or Control System

Tuner app automatically

tunes control systems from

high-level design goals

(reference tracking,

disturbance rejection, and

stability margins)

• Tune control system

regardless of control system

architecture and/or the

number of feedback loops

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Fine tune controller gains using response optimization

Use Simulink Design Optimization to optimize overall system

response against requirements in the time and frequency domain

• Optimize model response

to satisfy design

requirements, test model

robustness

• Optimize time and

frequency-domain design

requirements

simultaneously, using

model verification blocks,

or custom constraints and

cost functions

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• Linearization of Plant

• Automatic PID Controller Tuning

• Gain Scheduling

• Multi-Loop Controller Tuning

• Response Optimization

• Model Predictive Control

AGENDA

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Model Predictive Controls

How MPC worksUses an internal plant model to predict future behavior

Solves a quadratic programming (QP) problem online

BenefitsMakes better decision with more knowledge of plant dynamics

Handles plant input and output constraints explicitly

Integrates both feedback and feed-forward control

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MPC Designer App

Design model predictive

controllers in MATLAB and

Simulink using improved

interactive workflows

Tune controller performance

using interactive sliders

Review MPC controllers for

design and stability issues

Compare the performance of

multiple MPC controllers

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Base/recommended control design tools

reference+

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controller

S1 S2

S3

Control System

Toolbox

Optimization

Toolbox

Simulink Control

Design

Simulink Design

Optimization

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Other control related products to

consider…

System Identification

Toolbox

Robust Control

Toolbox

Stateflow

Model Predictive

Control Toolbox

Global Optimization

Toolbox

Neural Network

Toolbox

specialized methods

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Other Resources

Designing Feedback Compensators and Control Logic:

http://in.mathworks.com/solutions/control-systems/designing-feedback- compensators-control-logic.html

Simulink Control Design Overviewhttp://in.mathworks.com/videos/simulink-control-design-overview-61203.html?s_tid=srchtitle

Simulink Design Optimization

http://in.mathworks.com/products/sl-design-optimization/

Model Predictive Control

http://in.mathworks.com/products/mpc/

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Training

MATLAB Fundamentals

Simulink for System and Algorithm Modeling

MATLAB and Simulink for Control Design Acceleration

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Q&A