Control Systems: Overview - Philadelphia University. Control Syst… · Bode plots Nyquist...

D R . T A R E K A . T U T U N J I

M E C H A C T R O N I C S Y S T E M D E S I G N

P H I L A D E L P H I A U N I V E R S I T Y

2 0 1 3

Control Systems: Overview

Outline

Basic Control Concepts

Control Techniques and Methods

Hardware Controllers

Control Systems

A control system is at the heart of mechatronic systems where electronics are used to control mechanical systems.

Open-Loop Control

[Ref] Kilian

Closed-Loop Control

[Ref] Kilian

Control Systems Classification

Control systems are classified by application.

Process control usually refers to an industrial process being electronically controlled for the purpose of maintaining a uniform correct output.

Motion control refers to a system wherein things move. A servomechanism is a feedback control system that provides remote control motion of some object, such as a robot arm or a radar antenna.

Process Control

[Ref] Kilian

Process Control Example

Motion Control

Motion Control Example: CNC Machine

[Ref] Kilian

Motion Control Example: Robotic System

[Ref] Kilian

Transfer Functions

Each component in the control system can be described mathematically by a transfer function (TF), where TF = output/input.

Transfer functions of individual components in a system can be mathematically combined to calculate overall system performance.

Transfer function includes transient and steady-state characteristics,

Transfer Functions

Example

[Ref] Kilian

General Block Diagram

[Ref.] Shetty

Basic Control Signals

[Ref.] Shetty

Basic Control Functions

[Ref.] Shetty

Performance Criteria

System Performance

Stability

Accuracy

Transient Response

Sensitivity

Stability

A stable system is one which produces a bounded, or finite, response when subjected to a bounded input

Stability conditions

A system is stable if the real part of all poles are < 0.

A system is marginally stable if real part of all poles are <= 0.

A system is unstable if the real part of any pole is positive.

Accuracy

Accuracy (or steady-state tracking error) is the error between input and output signals in the steady state for a system.

Three input signals can be used

Step

Ramp

Parabola

Accuracy

Transient Response

Transient response is the shape of a signal as it moves between two steady-state points.

It is quantified in terms of two parameters:

The damping ratio, z, pronounced zeta

The natural undamped frequency, wn.

Pole Locations

[Ref.] Shetty

Sensitivity

Sensitivity is the measure by which controlled signals are influenced by disturbances which include parameter variations within the plant and external signals such as noise.

Control Techniques

T A R E K A . T U T U N J I

Dr. Tarek A. Tutunji

Control Techniques / Strategies

Classical Control

Adaptive Control

Robust Control

Optimal Control

Intelligent Control


Classical Control

Classical control design are used for SISO systems.

Most popular concepts are:

Bode plots

Nyquist Stability

Root locus.

PID is widely used in feedback systems.

Classical Control: On-Off Control

This is the simplest method of control. The control action has three possible outputs: on; off; no change. This method is usually used for slow-acting operations (such as a refrigeration unit).

The advantage is its ease of design and low cost. However, it cannot vary the controlled variable with precision.

On-Off Control Example


Classical Control: PID

Proportional-Integral-Derivative (PID) is the most commonly used controller for SISO systems

dt

)t(deKdt)t(eK)t(eK)t(u DIp

Analog PID Implementation

[Ref] Kilian

Discrete PID Implementation

[Ref] Kilian

Classical Control: Root Locus

Classical Control: Compensators

Classical vs. Modern Control

In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation.

A mathematical model of a physical system as a set of

input, output and state variables related by first-order differential equations.

The variables are expressed as vectors and the differential

and algebraic equations are written in matrix form.

The state space representation provides a convenient and compact way to model and analyze systems with multiple inputs and outputs.

Adaptive Control

Adaptive control involves modifying the control law used by a controller to cope with the fact that the parameters of the system being controlled are slowly time-varying or uncertain.

Such controllers use on-line identification of the

process parameters. For example, as an aircraft flies, its mass will slowly

decrease as a result of fuel consumption; we need a control law that adapts itself to such changing conditions.

Robust Control

Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design.

Robust control methods are designed to function

properly so long as uncertain parameters or disturbances are within some set.

The state-space methods were sometimes found to

lack robustness, prompting research to improve them. This was the start of the theory of Robust Control, which took shape in the 1980's and 1990's and is still active today.

Adaptive vs. Robust Control

Adaptive control does not need a priori information about the bounds on uncertainties or time-varying parameters.

Robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is precisely concerned with control law changes.

Optimal Control

Optimal control is a set of differential equations describing the paths of the state and control variables that minimize a “cost function”

For example, the jet thrusts of a satellite needed to bring it to desired trajectory that consume the least amount of fuel.

Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability. Model Predictive Control (MPC)

Linear-Quadratic-Gaussian control (LQG).


Intelligent Control

Intelligent Control is usually used when the mathematical model for the plant is unavailable or highly complex.

Intelligent controllers are also used when the system must make decisions (from several alternatives) based on input data from sensors

The most two commonly used intelligent controllers are

Artificial Neural Networks

Fuzzy Logic

Intelligent Control: Fuzzy

Fuzzy set theory provides mathematical tools for carrying out approximate reasoning processes when available information is uncertain, incomplete, imprecise, or vague.

Fuzzy logic controllers manage complex control problems through heuristics (IF … THEN) and mathematical models provided by fuzzy logic, rather than via mathematical models provided by differential equations.

This is particularly useful for controlling systems whose mathematical models are nonlinear or for which standard mathematical models are simply not available

Fuzzy Control

Intelligent Control: ANN

Artificial Neural networks (ANN) are nonlinear mathematical models that are used to mimic the biological neurons in the brain.

ANN are used as black box models to map unknown functions

ANN can be used for: Identification and Control


ANN: Single Neuron

y

w0

w1

wM

x1

x2

xM

f(net)

M

mmmwxfy

1

Neural Nets

TDL

TDL

Weights

Weights

Log

Function + Weights +

Log

Function

Plant

Output

Plant

Input

Net

Output

First Layer Second Layer

ANN: Identification and Control

Identification Control

ANN: Identification and Control

D R . T A R E K T U T U N J I


Analog vs. Digital Control Systems

Analog Digital

Time variable Continuous Discrete

Time equations Differential equations Difference equations

Frequency transforms Laplace Z-Transform

Stability Poles on LHS Poles inside unit circle

Controller Hardware: Op-Amps Software: None

Hardware: Microcontroller Software: Program


Digital Control Block Diagram

Criteria for Choosing Controller

Price Size and Weight Number of Digital Inputs and Outputs Number of Analog Inputs and Outputs Speed Required Interrupt Required hardware Communication Interface Reliability Memory Programming Capability Software Support



Microcontroller

PLCs

DSPs

FPGA

PC with DAQ


Microcontrollers

Microcontroller is a special type of small computer that can perform a specific job

Microcontrollers

The microcontroller is a computer-on-chip. It is an integrated circuit that contains microprocessor, memory, I/O ports and sometimes A/D converters. It can be programmed using several languages (such as Assembly or C/C++). It can be used in manufacturing lines, but requires additional hardware. Microcontrollers are mainly used in engineering products such as washing machines and air-conditioners.


Microcontrollers Companies

Microcontroller Market Share

Arduino

Arduino is an open-source electronics prototyping platform based on flexible, easy-to-use hardware and software.

The hardware consists of a simple open source hardware board designed around an 8-bit Atmel AVR microcontroller, though a new model has been designed around a 32-bit Atmel ARM

ARM

The ARM architecture describes a family of RISC-based computer processors designed and licensed by British company ARM Holdings.

As an IP core business, ARM Holdings itself does not manufacture its own electronic chips, but licenses its designs to other semiconductor manufacturers

PLCs

A Programmable Logic Controller (or PLC) is a specialized digital controller that can control machines and processes. it monitors inputs, makes decisions, and controls outputs in order to automate machines and processes

Programmable Logic Controller

PLC’s are a user-friendly, microprocessor-based, specialized computer that is used for process control. It contains input/output (I/O) modules for appropriate sensors/actuator interfaces. It is mainly used in automated manufacturing lines. The PLC is usually used for simple logic operations. It is considered reliable and easy to program (using ladder diagrams, instructions, or function blocks).


PLC Manufacturers

PLC vs. Microcontroller

Usually PLCs are used in an industrial environment, where as the microcontrollers are smaller and well suited for embedded situations.

PLCs are programmed with ready made blocks or programming elements, whereas in Microcontrollers a programming language must be used to write a programming code

PLC Advantages

They are highly reliable, fast and flexible.

They can handle severe conditions such as dust, humidity etc.

They can communicate with other controllers.

They are easy to program and troubleshoot.

They include display units.

Digital Signal Processors

Digital Signal Processing (DSP) is the arithmetic processing of discrete-time signals. A/D is needed for analog signals

Digital signal processors (DSP) are specialized microprocessors with

advanced architectures (such as multiple buses, parallel processing, hardware multipliers and fast sampling rate) that are designed to reduce the number of instructions and operations necessary for efficient processing.

DSP chips enable developers to implement complex algorithms and

perform computationally efficient and fast algorithms. DSP are preferred over microcontrollers when the need for complex and iterative

control algorithms is required.

The term “Digital Signal Controllers (DSC)” refers to the use of DSP as control elements


Commonly used DSP Operations

Convolution

Correlation

Fourier Transform

Power Spectrum

Digital Filtering


DSP Operations: Convolution Consider a system h(n) with input x(n) and output y(n)

h(n)

x(n) y(n)

X(Z)H(z)Y(Z)

h(n)*x(n)y(n)

Then,

The convolution of two signals, x(n) and h(n), is given by

-k

k)x(n)h(nh(n)*x(n)y(n)

•One signal is flipped and shifted with respect to the other . •Each element of one signal is multiplied by the corresponding element of the other. •All the elements are summed. •Correlation requires a lot of calculations.


DSP Architecture Features

Parallel Processing (Modified Harvard)

Deep Instructions Pipeline

Very Fast A/D

Hardware Multiplier

Barrel Shifter

RISC


Modified Harvard Architecture

A Harvard architecture employs separate program and data buses to access separate data and program memories.

A modified Harvard architecture.

DSP use multiple data buses (and multiple associated address buses) so that the processing of two signals can be done in parallel.

The address buses are also separate. This multiple bus arrangement increases speed since instructions and data can move in parallel, and execute simultaneously rather than sequentially.

Modified Harvard Architecture

DAGEN A

DAGEN B Memory

A Memory

B

ALU Multiplier

Shifter

Accumulators

Shifter Memory

C

DAGEN C

Instruction Pipelining

Up to six levels of pipelining are implemented.

DSP can execute instructions in parallel

Overall execution times are accelerated so that high

Hardware Multiplier

A 16- by 16-bit hardware multiplier multiplies and stores results in a 40-bit accumulator (8 guard bits) in a single instruction cycle.

Thus, multiply and accumulate operations can be performed in a single clock cycle in a DSP; conventional processors may require tens of cycles for this operation.

Shifters and RISC

Hardware shifters allow scaling, prevent overflows, and maintain required precision.

An on-chip hardware stack reduces interrupt response time and minimizes stack pointer manipulations.

DSP use reduced instruction sets tailored to digital signal processing operations. For example, the MACD command implements four operations in one instruction: multiplies two values moves data adds the product to a previous result transfers the result to an adjacent register.

Digital Signal Controllers Manufacturers

Texas Instruments.

TMS320C2000™ DSP Platform

Microchip.

dsPIC30F3010

Motorola

Custom made DSP Engines

Field Programmable Gate Arrays

The field-programmable gate array (FPGA) is a semiconductor device that can be programmed after manufacturing.

Instead of being restricted to any predetermined hardware function,

an FPGA allows you to program product features and functions, adapt to new standards, and reconfigure hardware for specific applications even after the product has been installed in the field—hence the name "field-programmable".

FPGAs can be used to implement any logical function that an application-specific integrated circuit (ASIC) could perform. One advantage is its ability to update the functionality after shipping.

FPGAs vs. Microcontrollers

FPGAs can perform concurrent operations while the microcontrollers’ operations are sequential. This makes FPGAs better suited for real-time applications such as executing

DSP algorithms.

FPGA are flexible, you can add subtract the functionality as

required. This can not be done in microcontroller. FPGAs are hard-wired and the random attack of alpha rays can not

destroy/corrupt the memory areas hence collapse the device functionality.

FPGA based development is longer while microcontrollers change

too often and there is lots re-work required to do in order to keep pace with changing technology. This is necessary to save the design from being obsolete.


FPGAs vs. Microcontrollers

The development time for microcontroller is shorter and that of FPGA

The microcontroller peripherals are readily available and tested by

the vendor. As for the FPGA, open source soft-peripherals are available, but still need to be embedded and tested.

Microcontroller are power efficient. Microcontroller are low-cost, much lower than FPGAs. This is

specially true for small applications and large quantities. Microcontrollers are available in easy to solder SOIC and QFP

package while FPGAs offer limited sources.


Personal Computers

Personal computers are used when extensive signal processing and in-depth analysis is required.

This will require Data Acquisition Cards (DAQs) to interface

the I/O power and signals between the PC and the environment.

Advantages include superior graphical and software

flexibility. However, the cost is high and, therefore, they are not suitable

for a large number of products Another disadvantage is the speed


PCs and DAQs

Summary

The selection of the controller is arguably the most important issue of the mecahtronics system

This choice can be divided into two parts:

1. Software/Firmware algorithm On-Off, PID, Adaptive, Robust, Optimal, and Intelligent

2. Hardware system Microcontroller, PLC, DSP, FPGA, and PC-DAQ


Control Systems: Overview - Philadelphia University. Control Syst… · Bode plots Nyquist...

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