This document summarizes the design process for developing a closed-loop feedback control system for an electronic throttle body. It involves:
1) Modeling the system to obtain the transfer function.
2) Analyzing the transfer function using MATLAB to determine if the system is stable or oscillatory.
3) Simulating an open-loop model to account for real-world non-idealities.
4) Designing a PD controller to meet specifications and stabilize the oscillatory system. The controller is tuned using MATLAB simulations.
5) Implementing the designed controller in a closed-loop system model in System Vision software.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Speed and Torque Control of Mechanically Coupled Permanent Magnet Direct Curr...IDES Editor
A new controller is designed for speed and torque
control of a Permanent Magnet DC motor based on
measurements of speed and current. This research work
focuses on investigating the effects of control of the speed and
torque of two brushless dc motors that are mechanically
coupled. Two controller design methods: the Root Locus
method and Bode Plot method as well as two controllers:
Proportional-Integral-Derivative (PID) and Proportional-
Integral (PI) are used to obtain the control objectives of speed
control and torque control. The simulation is performed using
MATLAB/SIMULINK software. The effects of varying the
controller gains on the system performance is studied and
quantified. The simulation results show that the speed control
objectives of the motor are satisfied even in the case of torque
disturbance from the other motor.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Speed and Torque Control of Mechanically Coupled Permanent Magnet Direct Curr...IDES Editor
A new controller is designed for speed and torque
control of a Permanent Magnet DC motor based on
measurements of speed and current. This research work
focuses on investigating the effects of control of the speed and
torque of two brushless dc motors that are mechanically
coupled. Two controller design methods: the Root Locus
method and Bode Plot method as well as two controllers:
Proportional-Integral-Derivative (PID) and Proportional-
Integral (PI) are used to obtain the control objectives of speed
control and torque control. The simulation is performed using
MATLAB/SIMULINK software. The effects of varying the
controller gains on the system performance is studied and
quantified. The simulation results show that the speed control
objectives of the motor are satisfied even in the case of torque
disturbance from the other motor.
Design and Implementation of an Electrical Lift Controlled using PLC IJECEIAES
This paper represents the possibility of controlling an electrical elevator model using PLC and studying some parameters to ensure its work, this model have been designed and constructed to perform a completed elevator work in an automating technique according to its programming and controlling method that making the connecting much more easier and safer than real relays and complicated wiring method. As well as the small DC motor drive (gear box) electrical motor that used to drive the elevator cabinet which made the transition from floor to floor much smoother and much efficient than the traditional elevators.
This work treats the modeling and simulation of non-linear system behavior of an induction motor using backstepping sliding mode control (BACK- SMC). First, the direct field oriented control IM is derived. Then, a sliding for direct field oriented control is proposed to compensate the uncertainties, which occur in the control. Finally, the study of Backstepping sliding controls strategy of the induction motor drive. Our non linear system is simulated in MATLAB SIMULINK environment, the results obtained illustrate the efficiency of the proposed control with no overshoot, and the rising time is improved with good disturbances rejections comparing with the classical control law.
Three phase induction motor Induction is one of the widest spread motor due to its
robustness, simple construction, no need for complex circuits for starting. With several
available speed control techniques, this paper presents a new Proportional-Integral (PI)
controller and Artificial Neural Network (ANNs) control system based on vector control
scheme. MATLAB/SIMULINK software may be used to create a 3phase induction engine
model. To achieve the effectiveness of the controller, the system is subjected to external
disturbance. Experimental results are presented and satisfied with the controller results.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
For Induction motor is a system that works at their speed, nevertheless there are applications at which the speed operations are needed. The control of range of speed of induction motor techniques is available. The robust control is used with induction motor and the performance of the system with the controller will be improved. The mathematical model to the controller, which were coded in MATLAB. The modeling and controller will be shown by the conditions of robustness of be less than one.
Speed control of Separately Excited DC Motor using various Conventional Contr...IJERA Editor
This paper presents comparative study of various conventional controllers such as Proportional (P), Proportional
Derivative (PD), Proportional integral (PI) and Proportional Integral Derivative (PID) controller for a speed
control of a Separately Excited Direct Current (SEDC) motor by using MATLAB / SIMULINK. All controllers
have their specific function for a particular task. The speed control normally done by feedback loop or closed
loop. The aim of development of this paper is towards providing efficient and simple method for controlling the
speed. The auto - tuning method are used to for this paper to control the speed. Among all this controllers PI
controller are frequently utilized in industries as compared to PID because Derivative action are sensitive to
noise, though PID controller will improve the steady state error. Additionally it produces less overshoot,
decreasing rise time and settling time. The MATLAB simulation are analysed and compared by using the auto
tuning method.
Keywords - Proportional (P), Proportional – Derivative (PD), Proportional - Integral (PI), Proportional –
Hardware-in-the-loop based comparative analysis of speed controllers for a tw...journalBEEI
A comparative study of speed control performance of an induction motor drive system connecting to a load via a non-rigid shaft. The nonrigidity of the coupling is represented by stiffness and damping coefficients deteriorating speed regulating operations of the system and can be regarded as a two-mass system. In the paper, the ability of flatness based and backstepping controls in control the two-mass system is verified through comprehensive hardware-in-the-loop experiments and with the assumption of ideal stator current loop performance. Step-by-step control design procedures are given, in addition, system responses with classical PID control are also provided for parallel comparisons.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Design and Implementation of an Electrical Lift Controlled using PLC IJECEIAES
This paper represents the possibility of controlling an electrical elevator model using PLC and studying some parameters to ensure its work, this model have been designed and constructed to perform a completed elevator work in an automating technique according to its programming and controlling method that making the connecting much more easier and safer than real relays and complicated wiring method. As well as the small DC motor drive (gear box) electrical motor that used to drive the elevator cabinet which made the transition from floor to floor much smoother and much efficient than the traditional elevators.
This work treats the modeling and simulation of non-linear system behavior of an induction motor using backstepping sliding mode control (BACK- SMC). First, the direct field oriented control IM is derived. Then, a sliding for direct field oriented control is proposed to compensate the uncertainties, which occur in the control. Finally, the study of Backstepping sliding controls strategy of the induction motor drive. Our non linear system is simulated in MATLAB SIMULINK environment, the results obtained illustrate the efficiency of the proposed control with no overshoot, and the rising time is improved with good disturbances rejections comparing with the classical control law.
Three phase induction motor Induction is one of the widest spread motor due to its
robustness, simple construction, no need for complex circuits for starting. With several
available speed control techniques, this paper presents a new Proportional-Integral (PI)
controller and Artificial Neural Network (ANNs) control system based on vector control
scheme. MATLAB/SIMULINK software may be used to create a 3phase induction engine
model. To achieve the effectiveness of the controller, the system is subjected to external
disturbance. Experimental results are presented and satisfied with the controller results.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
For Induction motor is a system that works at their speed, nevertheless there are applications at which the speed operations are needed. The control of range of speed of induction motor techniques is available. The robust control is used with induction motor and the performance of the system with the controller will be improved. The mathematical model to the controller, which were coded in MATLAB. The modeling and controller will be shown by the conditions of robustness of be less than one.
Speed control of Separately Excited DC Motor using various Conventional Contr...IJERA Editor
This paper presents comparative study of various conventional controllers such as Proportional (P), Proportional
Derivative (PD), Proportional integral (PI) and Proportional Integral Derivative (PID) controller for a speed
control of a Separately Excited Direct Current (SEDC) motor by using MATLAB / SIMULINK. All controllers
have their specific function for a particular task. The speed control normally done by feedback loop or closed
loop. The aim of development of this paper is towards providing efficient and simple method for controlling the
speed. The auto - tuning method are used to for this paper to control the speed. Among all this controllers PI
controller are frequently utilized in industries as compared to PID because Derivative action are sensitive to
noise, though PID controller will improve the steady state error. Additionally it produces less overshoot,
decreasing rise time and settling time. The MATLAB simulation are analysed and compared by using the auto
tuning method.
Keywords - Proportional (P), Proportional – Derivative (PD), Proportional - Integral (PI), Proportional –
Hardware-in-the-loop based comparative analysis of speed controllers for a tw...journalBEEI
A comparative study of speed control performance of an induction motor drive system connecting to a load via a non-rigid shaft. The nonrigidity of the coupling is represented by stiffness and damping coefficients deteriorating speed regulating operations of the system and can be regarded as a two-mass system. In the paper, the ability of flatness based and backstepping controls in control the two-mass system is verified through comprehensive hardware-in-the-loop experiments and with the assumption of ideal stator current loop performance. Step-by-step control design procedures are given, in addition, system responses with classical PID control are also provided for parallel comparisons.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
STATOR FLUX OPTIMIZATION ON DIRECT TORQUE CONTROL WITH FUZZY LOGIC cscpconf
The Direct Torque Control (DTC) is well known as an effective control technique for high
performance drives in a wide variety of industrial applications and conventional DTC technique
uses two constant reference value: torque and stator flux. In this paper, fuzzy logic based stator
flux optimization technique for DTC drives that has been proposed. The proposed fuzzy logic
based stator flux optimizer self-regulates the stator flux reference using induction motor load situation without need of any motor parameters. Simulation studies have been carried out with Matlab/Simulink to compare the proposed system behaviors at vary load conditions. Simulation results show that the performance of the proposed DTC technique has been improved and especially at low-load conditions torque ripple are greatly reduced with respect to the conventional DTC
Optimization of Modified Sliding Mode Controller for an Electro-hydraulic Act...IJECEIAES
This paper presents the design of the modified sliding mode controller (MSMC) for the purpose of tracking the nonlinear system with mismatched disturbance. Provided that the performance of the designed controller depends on the value of control parameters, gravitational search algorithm (GSA), and particle swarm optimization (PSO) techniques are used to optimize these parameters in order to achieve a predefined system’s performance. In respect of system’s performance, it is evaluated based on the tracking error present between reference inputs transferred to the system and the system output. This is followed by verification of the efficiency of the designed controller in simulation environment under various values, with and without the inclusion of external disturbance. It can be seen from the simulation results that the MSMC with PSO exhibits a better performance in comparison to the performance of the similar controller with GSA in terms of output response and tracking error.
Explicit model predictive control of fast dynamic systemeSAT Journals
Abstract Explicit Model Predictive Control approach provides offline computation of the optimization law by Multi Parametric Quadratic Programming. The solution is Piece wise affine in nature. It is explicit representation of the system states and control inputs. Such law then can be solved using binary search tree and can be evaluated for fast dynamic systems. Implementing such controllers can be done on microcontroller or ASIC/FPGA. DC Motor Speed Control - one of the benchmark systems is discussed here in this context. Its PWA law obtained, simulation of closed loop e-MPC is presented and its implementation approach using MPT toolbox and other such toolboxes is shown in brief. Index Terms: Model Predictive Control, explicit, Piece-wise Affine, and Multi Parametric Toolbox
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Sliding mode control-based system for the two-link robot armIJECEIAES
In this research, the author presents the model of the two-link robot arm and its dynamic equations. Based on these dynamic equations, the author builds the sliding mode controller for each joint of the robot. The tasks of the controllers are controlling the Torque in each Joint of the robot in order that the angle coordinates of each link coincide with the desired values. The proposed algorithm and robot model are built on Matlab-Simulink to investigate the system quality. The results show that the quality of the control system is very high: the response angles of each link quickly reach the desired values, and the static error equal to zero.
A Novel Technique for Tuning PI-controller in Switched Reluctance Motor Drive...IJECEIAES
This paper presents, an optimal basic speed controller for switched reluctance motor (SRM) based on ant colony optimization (ACO) with the presence of good accuracies and performances. The control mechanism consists of proportional-integral (PI) speed controller in the outer loop and hysteresis current controller in the inner loop for the three phases, 6/4 switched reluctance motor. Because of nonlinear characteristics of a SRM, ACO algorithm is employed to tune coefficients of PI speed controller by minimizing the time domain objective function. Simulations of ACO based control of SRM are carried out using MATLAB /SIMULINK software. The behavior of the proposed ACO has been estimated with the classical Ziegler- Nichols (ZN) method in order to prove the proposed approach is able to improve the parameters of PI chosen by ZN method. Simulations results confirm the better behavior of the optimized PI controller based on ACO compared with optimized PI controller based on classical Ziegler-Nichols method.
CONTROL OF AN INDUCTION MOTOR WITH DOUBLE ANN MODEL BASED DTCcsandit
Direct torque control (DTC) is preferably control method on high performance control of induction motors due to its dvantages such as fast dynamic response, simple and robust control structure. However, high torque and current ripples are mostly faced problems in this control method. This paper presents artificial neural network (ANN) based approach to the DTC method to overcome mentioned problems. In the study, by taking a different perspective to ANN and DTC integration, two different ANN models have been designed, trained and implemented. The first ANN model has been used for switch selecting process and the second one has been used for sector determine process. Matlab/Simulink model of the proposed ANN based DTC method has created in order to compare with the conventional DTC and the proposed DTC
methods. The simulation studies have proved that the induction motor torque and current
ripples have been reduced remarkably with the proposed method and this approach can be a
good alternative to the conventional DTC method for induction motor control
Similar to Unity Feedback PD Controller Design for an Electronic Throttle Body (20)
CONTROL OF AN INDUCTION MOTOR WITH DOUBLE ANN MODEL BASED DTC
Unity Feedback PD Controller Design for an Electronic Throttle Body
1. 2006 ERNST & SAPUTRA
Unity Feedback PD ControllerUnity Feedback PD ControllerUnity Feedback PD ControllerUnity Feedback PD Controller
Design for anDesign for anDesign for anDesign for an ElectronicElectronicElectronicElectronic
Throttle BodyThrottle BodyThrottle BodyThrottle Body
2. 2006 ERNST & SAPUTRA
1.0.0. Abstract
his project report examines the design of an electronic throttle body and applies a control
system to stabilize and control the response. This design can be broken up into four primary
categories. The initial stage is to obtain information about the system and organize the
material in a manner useful for control development (identifying the transfer function). This involves
developing the frequency-domain block diagram for the system. This is done by analyzing the
equations of motion and implementing them into the current system. Additionally, the transfer function
equation is obtained from the block diagram to be used for design and modeling.
Once the necessary information has been obtained from the system, the development of a controller
can begin. Using the transfer function obtained from the block diagram, the use of software analysis
(such as MATLAB) can be used to identify the characteristics of the existing system. This can allow a
controls engineer to encounter any points of instability within the system that may have been
overlooked. In addition to identifying points of concern within the system (ie: oscillation from poles on
the jù axis), the software application can be used to identify what type of control system, whether it is
P, PD, PI, or PID, will and will not be a reasonable means for their application. From there, a
controller with general specifications can be chosen.
The next stage in the process of developing a closed loop feedback control system for an electronic
throttle body is to simulate an open loop system model of the plant without additional control. This
allows you to account for any unforeseen problems that the system might encounter. This stage is
crucial for the fact that you identify the limitations of your model (ie: the min to max position of the
plate angle). An open loop system model will allow the controls engineer an opportunity to identify
additional elements that may be necessary in the final stages of development for their controller.
Now that the stability of your system is identified in a static and dynamic atmosphere, the final design
can be developed. The final design would be a closed loop feedback control system. After including
the controller to the system, the system characteristics (ie: rise time, overshoot) may not be at the
desired level. Because of this, adjustments must be made in order to meet the specifications of the
consumer. Once the controller has been tuned to obtain the desired result, the actual implementation
onto the electronic throttle body would begin.
2.0.0. Introduction
n the early 1980s, electronic throttle body was introduced as a transition technology to fully
electronic port injection. The electronic throttle body (ETB) has no linkage connection
between the throttle pedal and ETB is required the use of an electric actuator motor. The
throttle body is a component within the engine that controls the amount of air into the induction
system. It also opens and closes the control device of the accelerator pedal effort. For several years,
there have been numerous commercial industries, such as the automotive industry, that has a large
interest in applying control system technology to this application. The increase in interest for this
application can be contributed to the opportunity to provide a state-of-the-art engine management
system that helps satisfy governmental regulations as well as customer demands.
The primary purpose of an electronic throttle body is to control the amount of airflow into the engine.
As part of the throttle body, a butterfly valve is used to open and close the passage into the intake
manifold in order to increase/decrease the volume of the air entering the engine. Our task is to
develop a control system to limit the amount of airflow allowed to enter the engine by adjusting the
position of the plate within the electronic throttle body. The control system will be required to obtain
the desired output rating while meeting the customer specifications for the rise time (<50 ms), settling
time (<250 ms), and overshoot (<25%) of the step response to the overall system. The specifications
for our specific controller design are: <25% overshoot, a settling time of <250ms, and a rise time of <
50ms.
3. 2006 ERNST & SAPUTRA
3.0.0. Model Description
3.1.0 The original system model
Components Name Description
Current Input
An Ideal controlled input used to supply power to
electric components in the system.
DC Motor
Electrical to rotational conversion unit used to
create an angular velocity that is sent to the gear
shaft.
Angular Velocity -> Angle
Converts the angular velocity to an angle. Angular
velocity is the derivative of orientation with respect
to time.
Gear / Gear Ratio
A toothed wheel designed to transmit and adjust
torque (valued at 59.0E-03).
Plate Inertia
The tendency of the plate at rest to remain at rest,
and of an object in motion to remain in motion.
Rotational Spring
A flexible elastic object used to store mechanical
energy based upon the position of the plate.
Rotational Reference
A static connection between points used to identify
dynamic motion in a rotational form.
Each of the components shown above is used in developing the original functional model
representation of a simple electronic throttle body.
4. 2006 ERNST & SAPUTRA
3.2.0 The modified model system model
Components Name Description
Voltage Pulse
An non-ideal controlled input used to
supply power to electric components in
the system.
DC motor
Electrical to rotational conversion unit
used to create an angular velocity that is
sent to the gear shaft.
Gear / Gear Ratio
A toothed wheel designed to transmit and
adjust torque (valued at 59.0E-03).
Stop Plate
Used to restrict the range of rotational
motion (0° - 90°).
Rotational Spring
A flexible elastic object used to store
mechanical energy based upon the
position of the plate.
Angle –to-Voltage
Converter
Conversion unit used to change a
measured input from an angular value into
voltage.
Rotational Reference
A static connection between points used
to identify dynamic motion in a rotational
form.
Proportional Derivative
(PD) Controller
A component of a system that makes the
system operate within desired limits (ie.
customer specifications).
Each of the components shown above is used in developing the modified functional model
representation of a simple electronic throttle body with a controller and feedback.
5. 2006 ERNST & SAPUTRA
4.0.0. Design Approach and Analysis & Results
4.1.1. Design Approach – Part 1
When we examined the above schematic, we first derived the frequency-domain block
diagram which followed by the resultant transfer function. To create this block diagram,
we applied all the rules of conservation of energy, momentum, and torque to develop
the relevant equations of motion (EOM). From the EOM we created a block diagram of
the system by using the given important values of the model: i, tK ,r , spK , mJ , pJ ,θ.
1. p
m
J
J J
r
= + 2. ( )
1 ( ) ( )
TK G sOut
In G s H s
+
=
+
3. ( )
( )
T
s
K
i s
τ
= 4. ( ) 1
( ) p
m
s
Js
J
r
θ
τ
=
+
5. 2
( ) 1
( )
s
s s
θ
θ
=
4.1.2. Analysis and Results – Part 1
From the EOM, we analyzed the system to determine the appropriate block diagram
and transfer function. Below our block diagram is the resultant transfer function.
The block diagram:
r
K
s
r
J
J
K
spp
m
t
++
=
2
)(
i(s)
Theta(s) or
sppm
t
KsJrJ
rK
++
= 2
)(i(s)
Theta(s) ,
where 17
059.
1
≈=r
4.2.1. Design Approach – Part 2
To design a control system, our first step was to perform an analysis of the plant
transfer function and obtain the results of a time response to a unit step input via
MATLAB.
Steps taken to design a control system:
1. Perform the analysis of the plant transfer function whiling obtaining the results to
a time response from a unit step input via MATLAB. Identify whether the plant
transfer function is stable, unstable, or oscillatory.
2. Perform a root locus analysis in MATLAB, apply a proportional controller, and
analyze the plants behavior as the gain varies.
3. Identify the appropriate controller for the system.
4. Include the controller to the plant and perform the time analysis.
6. 2006 ERNST & SAPUTRA
5. Simulate the controller while apply a sweep of gain values.
4.2.2. Analysis and Results – Part 2
We performed an analysis of the plant transfer function and a time response to a unit
step input by using MATLAB.
The root locus shown above demonstrates how the system is expected to design
when the gain is varied. In other words, if you were to include a proportional controller
and change the K value of it, you will notice how the system changes. According to our
representation of the system, the poles will never leave the jω axis and therefore will
remain oscillatory regards of the proportional gain that is included into the system. This
can be seen in the image to the right, where the time response continues to oscillate
around 0.5. This response identifies a P controller as not the ideal controller this
application.
It can be seen in the time response that the plant is oscillatory. The throttle plate
inertia and dc motor inertia are the two components of the plant that cause the
oscillation to occur. Oscillation occurs when a second (or higher) order system is
introduced into the transfer function. From the transfer function, the combination of Jm
and Jp are what determine whether or not the system results in a second order
characteristic equation. When (Jm + Jp/r) becomes zero, the characteristic equation is
no longer second order. Therefore, the dc motor and the throttle plate are the two
physical components of the plant that cause it to behave this way.
Applying a proportional controller will not work because for any value of ‘k’ the poles of
the system will remain on the jω axis. In order for our controller to work more
effectively, we need to add a zero to our system.
We chose to use a PD (Proportional Derivative) controller. We chose a PD controller
because when including a derivative term, the poles will be located would be on the
LHP (Left Half Plane). Therefore, they will not remain on the jω axis as the gain is
varied and the system will no longer oscillate. PD Controller: (KDs + KP). Someone
could include a PID (Proportional Integral Derivative) controller as well. When looking
at the root locus, a PID controller places all the poles on the LHP. A PI (Proportional
Integral) controller would not work because it causes the poles of the system to result
in the RHP (Right Half Plane) which will make the system unstable.
After performing an analysis, we put the transfer function into MATLAB and
manipulated our zero that we added the following to our result: PD Controller: (0.233*s
+ 233). With this zero included into our MATLAB simulation, we were able to achieve
the specification of the customers.
Plant Transfer Function Analysis: Time Response to a Unit Step Input:
sys=tf([-.0187],[(-4.0295*10^-6) 0 -.003182]);
rltool(sys)
(additional option with rltool)
7. 2006 ERNST & SAPUTRA
Root Locus Editor Step Response
PD Controller: (KDs + KP)
The next controller we chose to look into is a proportional/derivate PD controller. When
using such a controller, it includes a pole to existing system. This is ideal for our
application because when the zero is place into the appropriate location, it will cause
the root locus lines to converge into the LHP and therefore increasing the stability of
our model.
After a location was found for the pole, we looked at the step response to identify the
system’s characteristics. With an overshoot of 14%, a rise time of 3.8 ms. and a settle
time of 25 ms, adding a pole at our desired location should exceed the specifications
from the customer. Below are three examples different attempts our group ran through
to end up learning the characteristics of the PD controller. The root locus editor
displays that result. Choosing gains for the controller and then simulates it. If you
adjust the value of Kp and Kt properly, you will be able to the customer specifications.
With Kd = .5 and Kp = .5* 10 = 5 With Kd = .005 and Kp = .005* 10 = 5
Transfer function:
0.5358 s + 5.358
--------------------------------
4.03e-006 s^2 + 0.5358 s + 5.361
Transfer function:
0.005358 s + 0.05358
------------------------------------
4.03e-006 s^2 + 0.005358 s + 0.05676
With Kd = .00005 and Kp = .00005* 10 = 5
8. 2006 ERNST & SAPUTRA
Transfer function:
5.358e-005 s + 0.0005358
---------------------------------------
4.03e-006 s^2 + 5.358e-005 s + 0.003718
As shown in the diagrams above, when increasing the derivative constant of your
controller, the settling time and rise time decreases, but the overshoot dramatically
increases. On the other hand, the increase in the overshoot can be compensated by
lowering the proportional gain constant. With this combination, a PD controller can be
tuned to the desired specifications.
4.3.1. Design Approach – Part 3
Now that our basic system model as well as a controller has been developed to meet
the customer’s specifications, our group continued onto the next stage of our design.
When looking at our electronic throttle body system on a real time basis, there are
additional elements in the model that are unaccounted for. The non-linear components
add additional poles and zeros to the system which in return can cause instability.
Fortunately, the use of System Vision software accounts for the dynamic behavior the
system will encounter allowing us to take this into consideration. With the use of
System Vision, we developed an open loop system model to determine the response
characteristics.
4.3.2. Analysis and Results – Part 3
In order to do simulate the electronic throttle body, additional modifications were
required to allow the system to be accurately modeled. The ideal current source is
replaced with a voltage pulse at 12v. Rather than applying an angular velocity motor
and later changing the angular velocity to angle, we install a motor that outputs the
9. 2006 ERNST & SAPUTRA
angle thus eliminating the previously shown conversion block. This motor contains the
following specifications: D=0, Winding Resistance = 2.8, Inertia = 4E-6, Inductance =
1.1E-3, and KT = 0.0187.
An additional modification is a rotational reference stop. This allows the system to
mimic the actual application into a System Vision simulation with better accuracy. The
final stage of our modification to our block diagram of the system was to ignore the
affects of the plate inertia. When looking into the original
equation,
r
K
s
r
J
J
K
spp
m
t
++
=
2
)(
i(s)
Theta(s)
you will notice that the inertia from the plate,
Jp, is far less significant than the inertia from the motor. Because of the fact
that 17
059.
1
≈=r , Jp can be ignored without viewing any significant difference in our
system. The reason for ignoring the additional component of our system is due to the
processing capabilities of our software (System Vision). Every time an additional
component is included, the software creates a sweep of every part in relation to the
other parts in the system. There every time an additional part is implemented, the
system has more to processing sweeps to account for.
Since System Vision accounts for the non-ideal situation, we can not duplicate the
oscillatory behavior shown previously in MATLAB. The ideal simulation in MATLAB
(root locus plot) demonstrates how the poles lie upon the jω axis. In the non-ideal
situation, this would not be the case. The pole would be drawn more into the left hand
plane (LHP), thus causing the oscillatory behavior to be reduced.
When variations of the input parameters where for the motor are changed, you can
notice a significant change in the how the plate reacts. Adjusting the magnitude, for
example, you will notice the overshoot response to act accordingly (a rise in the
magnitude will result in a rise in the overshoot).
Angular Velocity vs. Time Plot Bode Plots (Magnitude and Phase)
When replacing the voltage source with the previously used ideal current source, the
oscillatory behavior returns. The characteristics of the ideal current source cause the
system to behave more as expected. Adding the more realistic voltage source is
essentially the same as adding a zero on the LHP. A zero would cause the root locus
line to converge more into the LHP, therefore increasing the system’s stability. The
inductive contribution from the motor could also be an additional factor in the
contribution of stabilizing the system.
10. 2006 ERNST & SAPUTRA
4.4.1. Design Approach – Part 4
Now that our basic system model and controller has been created as well as modeled,
we can begin the final stage of developing a closed loop feedback controller system.
As shown in the second stage of our design, a PD and PID controller are both feasible
options to obtain our desired results. We have chosen to implement a PD controller
and model the characteristics via System Vision.
4.4.2. Analysis and Results – Part 4
Our design involved an angle to signal (Q) sensor, a signal to voltage sensor, a
differential block, a summation block, a proportional controller, and a derivative
controller. The first three devices mentioned were used to tie back the resultant output
to the input causing unity feedback. The additional three devices where used to
develop the PD control.
From adding a pole to the system in our MATLAB analysis, we selected one of the
many possible points of stabilization for our controller; we have chosen our PD
controller to be (0.233s + 233). After including this controller design to our system, the
resultant rise time and settling time met the customer specifications. However, the
overshoot from the response was not with the acceptable range. Therefore, (knowing
of the effects of a proportional controller) we choose to lower our proportional constant
from 233 to 20. This put our P/D ratio from 100 to 10.
Our electronic throttle body with the unity feedback and control (0.233s + 20) gives a
time response with the following characteristics: overshoot = 7.4699%, settling time =
2.3333 ms, rise time = 1.1137 ms all of which lye well into the range of the customer
specifications.
Step Response of the electronic throttle body with our PD controller (PD Controller: 0.233s + 20)
11. 2006 ERNST & SAPUTRA
Conclusions
From the development of a system model to the controller selecting and testing, this project
encompassed a large variety of aspects/techniques used in the industry. We began with deriving the
frequency-domain block diagram from the model of a widely used mechanical/electrical element.
From our block diagram, we develop the resultant transfer function so we can design a control system
with the assistance of such software as MATLAB and System Vision. Additionally, we included and
replaced some components as requested, such as replacing the ideal current source to the voltage
pulse component at 12v, using the angle output motor to eliminate the conversion component, and
adding the inductance and the stops. As a result from the process, we have developed a PD
controller that exceeds the specifications:
Customer
Specifications
PD Controller
Output Response
Overshoot (%OS) < 25 % 7.4699 %
Rise Time (TR) < 0.05 sec 0.001137 sec
Settling Time (TS) < 0.25 sec 0.0023333 sec
These objectives have been met by the following PD Controller: KD*s + KP = ( 0.233*s + 20 )
12. 2006 ERNST & SAPUTRA
6.0.0 Appendix
6.1.1 Questions & Answers
Questions Answers
Perform analysis of the plant transfer function itself in
MATLAB. Is the plant stable, unstable, or oscillatory?
The plant is oscillatory. The throttle plate inertia and dc
motor inertia are the two components of the plant that cause
the oscillation to occur. Oscillation occurs when a second
(or higher) order system is produced. From the transfer
function, the combination of Jm and Jp are what deplict
whether or not the system results in a second order
characteristic equation. When (Jm + Jp/r) becomes zero, the
characteristic equation is no longer second order. Therefore,
the dc motor and the throttle plate are the two physical
components of the plant that cause it to behave this way.
Perform a root locus analysis in MATLAB. This applies a
gain to the system, a proportional controller, and analyzes
the plants behavior for varying gains. Will a proportional
controller work for this system? Why? If not, what must your
controller add to work more effectively? HINT: Examine the
pole locations.
No, a proportional controller will not work because for any
value of ‘k’ the poles of the system will remain on the jω
axis. In order for our controller to work more effectively, we
need to add a zero to our system.
Pick a controller. Given the above analysis, which
controllers should work? Why? HINT: Examine what the
controllers add to the loop, these are the “knobs” you can
turn to affect performance. What does each knob affect?
We chose to use a PD (Proportional Derivative) controller.
We chose a PD controller because when including a
derivative term, the poles will be located would be on the
LHP (Left Half Plane). Therefore, they will not remain on the
jω axis as the gain is varied and the system will no longer
oscillate. PD Controller: (KDs + KP). Someone could include
a PID (Proportional Integral Derivative) controller as well.
When looking at the root locus, a PID controller places all
the poles on the LHP. A PI (Proportional Integral) controller
would not work because it causes the poles of the system to
result in the RHP (Right Half Plane) which will make the
system unstable.
Attach your controller to the plant and again perform time
analysis.
After performing an analysis, we put the transfer function
into MATLAB and manipulated our zero that we added to
the following result: PD Controller .233*s + 233
With this zero, we were able to achieve the specification of
the customers.
(Please see Math Analysis for this question)
Choose some gains for your controller and simulate. How
does it perform? Are you able to meet customer
specifications? Why or why not? What physical components
of the plant are directly affecting your controller? HINT:
Examine the pole locations symbolically. Which values are
the most affective? Physically, why is this so?
Please see: 4.2.2. Analysis and Results – Part 2
13. 2006 ERNST & SAPUTRA
The following are Step Response Curves from System Vision demonstrating the effects of our closed loop
feedback controller design.
Step Response with the Initial PD Controller: (0.233s + 233)
Time Response with the Finalized PD Controller: (0.233S + 20)
14. 2006 ERNST & SAPUTRA
Below is the output code used when running the simulation of our finalized PD controller.
=====> Saved and checked schematic : theschematic.1
VHDL-AMS netlisting succeeded.
Generating Spice with command c:mentorgraphicsSystemVision4.2wvwin32binsvspice.exe -_ -h -
kc:mentorgraphicsSystemVision4.2standardwspice.cfg -gtheschematic.tempfile theschematic
Wirelisting theschematic into file genhdltheschematictheschematic.cir.
Warning: No ground node (Label a net GND)
Post-Processing...
0 error(s) and 1 warning(s) in file theschematic.cir.
Netlisting completed : theschematic
Simulating the design theschematic with the library Z:MyProjectsim_admstheschematicWORK_AMS41
---------------------------------------
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vasetlib -prod pr
Z:MyProjectsim_admstheschematicWORK_AMS41
Modifying adms.ini
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr WORK_AMS41
Z:MyProjectsim_admstheschematicWORK_AMS41
Modifying adms.ini
Adding logical reference "WORK_AMS41" to directory "Z:MYPROJECTSIM_ADMSTHESCHEMATICWORK_AMS41"
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
Modifying adms.ini
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr FUNDAMENTALS_VDA
c:/mentorgraphics/SystemVision4.2/sim/systemvision/win32/Libraries/Fundamentals_VDA/lib/v4.1_1.1/Fundamentals_VDA
Modifying adms.ini
Adding logical reference "FUNDAMENTALS_VDA" to directory
"C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32LIBRARIESFUNDAMENTALS_VDALIBV4.1_1.1
FUNDAMENTALS_VDA"
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr SPICE2VHD
c:/mentorgraphics/SystemVision4.2/sim/systemvision/win32/Libraries/Spice2VHD/lib/v4.1_1.1/Spice2VHD
Modifying adms.ini
Adding logical reference "SPICE2VHD" to directory
"C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32LIBRARIESSPICE2VHDLIBV4.1_1.1SPICE2V
HD"
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
Compilation not required : theschematic
Simulating using cmd file : Z:/MyProject/sim_adms/theschematic/expt1.cmd
Including spice file : Z:MyProjectgenhdltheschematictheschematic.cir
Software under License
Copyright Mentor Graphics Corporation
***** ANALYSIS ....
***** 0 error(s).
***** 0 warning(s).
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSSTD.standard
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.math_real
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.fundamental_constants
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.electrical_systems
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.mechanical_systems
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.gear_r(ideal)
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.spring_r(linear)
15. 2006 ERNST & SAPUTRA
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.stop_r(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.dcmotor_r(basic)
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.v_pulse(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.q_from_angle(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.q_to_voltage(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_difference(behavioral
)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_deriv(s_dmn)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_gain(behavioral)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_sum(behavioral)
***** GENERATION ...
Warning 113: NODE "ELECTRICAL_REF": Not connected to any element.
This node has been removed from the netlist.
Warning 113: NODE "ROTATIONAL_REF": Not connected to any element.
This node has been removed from the netlist.
***** 0 error(s).
***** 2 warning(s).
INFORMATION ABOUT COMPILATION...
Memory space allocated (bytes): 361066
11 elements
8 nodes
0 input signals
EldoHDL VERSION : ELDO v6.4_1.1 (Production version) Tue Jun 14 16:32:26 GMT 2005
*** DATE: 02-Dec-2005 01:10:26
*** TITLE: * Command file for design: theschematic
TEMPERATURE : 27.000000 degrees C
Searching Operating Point between -1.000000e+013V and
1.000000e+013V
Performing DC analysis...
--> Partitioning circuit...
***> DC CPU TIME 0s 000ms <***
DC:1 iterations FOR DC analysis
ERNST_SAPUTRA 0.0
FEEDBACK 0.0
INPUT 0.0
N1N37 0.0
N1N65 0.0
N1N67 0.0
N1N69 0.0
N1N83 0.0
EldoHDL NEWTON: VNTOL=1.000000e-007 RELTOL=5.000000e-005
Compute from 0.000000 Nano to 2.500000E+007 Nano
***>Current simulation completed
SIMULATION INFORMATION
memory size allocated in bytes 738947
Latency: 0.000000%
16. 2006 ERNST & SAPUTRA
average number of iterations: 1.000000
nb of components: 11
nb of nodes: 8
nb of MOS or BIP calls: 0
Number of steps computed: 10666
***>CPU TIME 1s 360ms <***
--- Simulation finished at time 25 ms
--- Nb of transactions 3
--- Nb of events 3
Simulation results stored in theschematic.2