Study Review on Nominal Characteristic Trajectory

Following Controller for Point-To-Point Positioning

Systems

Fitri Yakub

Department of Mechanical Precision Engineering,

Malaysia-Japan International Institute of Technology,

Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia

irtif_81@yahoo.com

Rini Akmeliawati

Department of Mechatronics Engineering,

International Islamic University Malaysia,

Kuala Lumpur, Malaysia

rakmelia@iium.edu.my

Abstract—This paper introduces study review on nominal

characteristic trajectory following (NCTF) controller as a

practical controller for point-to-point (PTP) positioning systems.

PTP is one type of precision positioning systems that required

high accuracy with a high speed, fast response with no or small

overshoot and robustness to parameter variations and

uncertainties. In PTP applications, parameter varies with the

payload and some friction may cause the instability of the

performances. In this case, the system performance is expected to

be the same or as close as its performance when the system is in

normal condition. PTP positioning systems need a good controller

to achieve high speed and high precision motion. However, it is

not easy to achieve high precision system because of non-

linearities and uncertainties exist in the motion control systems.

A NCTF controller as a practical controller for PTP had been

proposed. The NCTF controller consists of two elements namely

a nominal characteristic trajectory (NCT) and a compensator. It

had been reported that the NCTF had a good positioning

performance and robustness to parameters variations.

Application of NCTF control for PTP positioning systems both

for one-mass system or multi-mass system are studied and

summarized. Fundamental concept of NCTF controller also

explained.

Keywords-NCTF; PTP; positioning system; controller

I. INTRODUCTION

Motion control systems play an important role in industrial

engineering applications such as advanced manufacturing

systems, semiconductor manufacturing systems, and computer

numerical control (CNC) machining systems. In general,

positioning systems can be classified into two types, namely

point-to-point (PTP) positioning systems and continuous path

(CP) control systems [1]. PTP positioning systems, either of

one-mass or multi-mass systems, is used to move an object

from one point to another point either in linear or angular

position.

PTP positioning systems requires high accuracy with a high

speed, fast response with no or small overshoot and robust to

parameter variations and uncertainties. Therefore, the most

important requirements in PTP positioning systems are the

final accuracy and transition time whereas the transient path is

considered as the second important. In PTP applications,

parameter varies with the payload and some friction may

cause the instability of the performances. In this case, the

system performance is expected to be the same or as close as

its performance when the system is in normal condition. Thus,

robustness is also an important requirement in order to

maintain the stability of the positioning systems.

Both types of motion control systems generally need a good

controller to achieve high speed and high precision motion.

However, it is not easy to achieve high precision system

because of non-linearities and uncertainties exist in the motion

control systems. One significant non-linearities is friction that

causes steady state error and/or limit cycles near the reference

position [2]. Another source of non-linearities in motion

control system is saturation of the actuator and/or electronic

power amplifier. Saturation causes slow motion and may

effect the stability of the performances [3]. Positioning

systems also characterized by parameter uncertainties that

caused by estimation error and/or parameter variations such as

inertia and friction variations.

Therefore, to achieve high and consistent performance, not

only the non-linearities effect, but also the uncertainties effect

should be considered in controller design process. However,

since there are non-linearities functions such as friction and

saturation cannot be compensated effectively by controller

design based on linear control theory.

In order to satisfy the design requirements, a good

controller is required. Many types of controllers have been

proposed and evaluated for positioning systems. The use of

proportional-integral-derivative (PID) controllers are the most

popular controller used in industrial control systems including

motion control systems due to their simplicity and also

satisfactory performances [4]. However, it is difficult to

achieve a fast response with no or small overshoot

simultaneously.

The model-based types of controllers such as controllers

with disturbance observer [5], time-optimal controller [6], and

sliding-mode controllers [7] have been proposed. These

controllers give good positioning performance and robust to

object uncertainties but the controller design requires

1945978-1-4577-2119-9/12/$26.00 c©2011 IEEE

modeling and conscious parameter identification process with

deep knowledge on modern control theory and design. To

overcome this problem, auto tuning controller also has been

studied in [8]. However, auto tuning method required an

iteration process and it was complicated, troublesome and time

consuming procedure.

On the other hand, an advanced and intelligent controllers

such as fuzzy logic controller and neural controller has been

studied by several researchers [9]. Both controllers do not

require an exact model and parameters of the object but in

fuzzy logic controllers, there are many adjustable elements

involved such as selection of membership functions and fuzzy

rules. Thus, it will increase the complexity of the design

process. In neural controllers also, there are no systematic

approaches to choose how many input and output needed and

the type of neural controller structure [10]. Generally, these

intelligent methods tend to be complex.

In practical applications, an engineer does not need deep

knowledge or be an expert in control systems theory while

designing controllers. Thus, easiness of controller design

process, simplicity of the controller structure and no

requirement of exact object model and its parameters are very

important and preferable in real applications. To achieve these,

nominal characteristic trajectory following (NCTF) controller

had been proposed as a practical controller for PTP

positioning systems in [11]. The controller design procedure is

simple and easily implemented since it is only based on a

simple open-loop experiment. In addition, an exact object

model and its parameters do not required while designing the

controller. Thus, this controller is easy to design, adjustable

and understands.

In this paper, the fundamental concept and design process of

the NCTF controller theories are explained in Section 2. The

applications of NCTF controller for one-mass system and two-

mass system are reviewed in Section 3 and 4 respectively.

Lastly, all the discussions are summarized in Section 5.

II. NCTF CONTROL CONCEPT

The NCTF controller was proposed in 2002 as a practical

controller for rotary one-mass PTP positioning system [12]. It

has been reported that NCTF controller for one-mass rotary

system has a better positioning performances and better

robustness to parameters variations than the conventional PID

controllers [12]. Its structure is shown in Fig. 1 consists of:

a) A nominal characteristic trajectory (NCT) that is

constructed based on measured , and , which were obtained

by a simple open-loop experiment. Thus, the NCT provides

information of characteristics of the system, which can be used

to design the PI compensator.

b) A compensator which is used to force the object motion

to reach the NCT as fast as possible, control the object motion

to follow the NCT, and end it at the origin of the phase-plane

(e = , e = 0) as shown in Fig. 2.

Therefore, the controller is called as the NCTF controller.

As shown in Fig. 1, the controller output is signal u. This

signal is used to drive the object. The input to the controller

are error, e, and object motion, . In principle, the controller

compares the object motion input, with the error-rate, e,

provided by predetermined NCT, at certain error. The

difference between the actual error-rate of the object and that

of the NCT is denoted as signal up, which is the output of the

NCT. If the object motion perfectly follows the NCT, the

value of signal up is zero. Thus, no action is performed by the

compensator. When the signal up is not zero, the compensator

is used to drive the value of signal up to zero.

Figure 1. Structure of NCTF control system

In Fig. 2, the object motion is divided into two phases; the

reaching phase and the following phase. During the reaching

phase, the compensator forces the object motion to reach the

NCT as fast as possible. Then, in the following phase, the

compensator controls the object motion to follow the NCT and

end at the origin. The object motion stops at the origin, which

represents the end of the positioning motion. Thus, the NCT

governs the positioning response performance.

Error, e

Err

or

rate

, e' NCT

o

Object motion

RP: Reaching phaseFP: Following phase

FP

RP

Figure 2. NCT and object motion

The electric motor is assumed as the actuator in this

discussion. To drive the object to reach the NCT, the actuator

needs to reach its maximum velocity. The characteristic of the

actuator when it stops from its maximum velocity influences

the final accuracy of the PTP positioning operation. Thus, this

characteristic is required to design the controller. In order to

obtain the required characteristics, conducting a simple open-

loop experiment is a simple and practical way.

In summary, the structure of the NCTF control system for

PTP positioning systems shown in Fig. 1 only works under the

following two conditions:

a) A DC or an AC servomotor is used as an actuator of the

object.

b) The reference input, r is constant and r = 0.

1946 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

The NCTF controller consists of NCT, which is

constructed based on a simple open-loop experiment of the

object, and PI compensator, which is designed based on the

obtained NCT. Therefore, the design of NCTF controller can

be described by the following steps:

a) A DC or The object is driven with an open loop

stepwise input and its displacement and velocity responses are

measured.

b) Construct the NCT by using the object responses

obtained during the deceleration process. Since the NCT is

constructed based on the actual responses of the object, it

contains non-linear characteristics such as friction and

saturation. The NCTF controller is expected to avoid

impertinent behavior by using the NCT.

c) Design the compensator based on the NCT information.

The NCT includes information of the actual object parameters.

Therefore, the compensator can be designed by using only the

NCT information.

III. ONE-MASS SYSTEM

Positioning systems generally consist of several elements

such as actuator, a gear, a shaft or spring and a load mass [12].

The systems can be modeled as one-mass positioning system

when a rigid coupling which is high stiffness is used. For

example, in application with one-mass system, such as CNC

machines, PTP positioning is used to accurately locate the

spindle at one or more specific locations to perform operations,

such as drilling, reaming, boring, tapping, and punching.

A. Linear System

In Fig. 3, the NCTF control method with anti-windup was applied to a ballscrew mechanism. Its structure consists of an

NCT and a PI as a compensator. The controller was designed without any exact identification of parameters or modeling. The practical stability limit is introduced rather than trial and error process to restrict the choice of design parameters for PI compensator within the stable area.

Figure 3. Ballscrew mechanism for one-mass linear system

The simulations and experiments verified that the NCTF controller design procedure is feasible for three additional cases [13]:

(a) when the damping of the mechanism changes, (b) when the Coulomb friction of the mechanism changes, (c) when the inclination of the NCT changes.

The intelligent based approach also had been used to

improve the performance of the NCTF controller with PI

compensator. The structure of fuzzy compensator, a fuzzy gain

was introduced. This gain amplifies the defuzzification control

output. The fuzzy gain value is defined as the maximum

velocity divided by the maximum actuator input rated. It is

usually a big positive number. Since the defuzzification

process is already based on actuator input rated, the output of

the fuzzy gain is out of actuator rated input. Therefore,

actuator saturation occurs[14]. The experimental has been

done for single axis linear system in Fig. 4. The rule base is

shown in Fig. 5. It had been shown that for the structure

without additional gain, the maximum control signal is within

the maximum actuator input rated. The experiment show that

the proposed practical fuzzy compensator is effective

compared with other NCTF controllers using different

compensators [14].

Figure 4. Ballscrew mechanism for one-mass linear system

Figure 5. Fuzzy rules

B. Rotary System

In the initial development of the NCTF controller, the

effectiveness of the controller was examined with

experimental one-mass rotary positioning system as shown in

Fig. 6. Its structure consists of an NCT and a PI as a

compensator. Simple controller design process has been

demonstrated and the controller performances have been

compared with PID controllers [15]. The robustness of the

controller due to inertia and friction variations has also been

evaluated. It has been shown that the controller is effective for

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 1947

positioning system and much more robust to inertia and

friction variations then the PID controller [15].

The performance of the NCTF controller with PI

compensator to compensate the effect of friction was

evaluated and compared with proportional and derivative (PD)

controller with a discontinuous non-linear proportional

feedback (DNPF) and PD controller with the smooth robust

non-linear feedback (SRNF). NCTF had achieved higher

accuracy and robustness against inertia and friction variation

compared to both type of PD controller. Thus, the NCTF

controller with PI compensator is effective to compensate for

the effect of the friction, which is the main source of

positioning inaccuracy [16].

The NCTF controller for one-mass rotary system has a

better positioning performances and better robustness to

parameter variations than the conventional PID controllers

[16].

Figure 6. Experimental mechanisms for one-mass rotary system

In order to eliminate a trial and error process in PI

compensator, a fuzzy-based NCTF control system had been

proposed [17]. Its structure consists of an NCT and a fuzzy

compensator. The structure of its fuzzy compensator is shown

in Fig. 7. A special gain called a fuzzy gain was placed at the

end after defuzzification process, and produced the control

signal to the actuator.

The simulation result using a dynamic model of one-mass

rotary positioning system showed that to a small step input the

response is similar with the response of NCTF controller with

PI compensator. Robustness evaluation has also been

examined to a small step input. The simulation indicated that

the robustness against inertia variation was as good as NCTF

controller with PI compensator [17].

Figure 7. NCTF control system with fuzzy compensator structure

The experimental results also confirmed effectively NCTF controller with fuzzy compensator can be applied to replace NCTF controller with PI compensator as shown in Fig. 8. This is due to the fact that fuzzy-based NCTF control has similar performances in terms of positioning performances and robustness to inertia variation; with the PI-based NCTF control, in addition to the ease design of fuzzy compensator [18].

Figure 8. Experimental mechanisms for one-mass rotary system

IV. TWO-MASS SYSTEM

Two-mass systems or multi-mass systems should be

modeled when flexible coupling or a long shaft are used. In

two-mass system applications, such as rolling mill drive, the

mechanical part of the drive has a very low natural resonant

frequency because of the large roll inertia and the long shaft

including the gear box and the spindle. Due to this, the finite

but small elasticity of the shaft gets magnified and has a

vibrational effect on the load position which may reduce

positioning accuracy [19]. Therefore, the existed NCTF

controller can not be used directly in the case there is a flexible

connection between elements of the positioning systems.

Improvements in the design of NCT and compensator are

required to make the NCTF controller is suitable for multi-

mass positioning systems

A. Linear System

The extension development of the NCTF controller has be

done experimentally for two-mass linear system as shown in

Fig. 9. Its structure consists of an NCT and a PI as a

compensator. The positioning performance of the system with

friction is examined in comparison with those of the system

with conventional PID controllers. The results prove that the

controller has a better positioning performance than those with

conventional PID controllers [20].

Figure 9. Two ball screw mechanisms

1948 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

Non-friction mechanism is often used for precision

positioning. Even though it has a simple structure, plant

identification still compulsory needed during designing a

conventional controller. This makes the controller non-user-

friendly and non-practical-used in industry. For overcoming

this problem, practical controller design procedure based on

NCT with a PI compensator, which is free from exact

modeling and parameter identification has been used [21].

The improvement in a practical NCTF controller which is

modified fast NCT (MFNCT) for fast positioning system has

been compared with conventional NCTF controller. It

confirmed that MFNCT is easy to use in NCTF controller

design while maintaining NCTF controller advantages of

design ease without known model parameters or much

knowledge of control theory. The NCTF controller with the

MFNCT has shorter rise and positioning times than with the

conventional NCT. The controller with the MFNCT shows the

same robustness to changes in movable mass and step height as

that with the conventional NCT, demonstrating that the

MFNCT and its design are useful for fast positioning [22].

B. Rotary System

The existing NCTF controller consists of a NCT and a

compensator. Both classical method using PI and intelligent

method using fuzzy compensator that were mentioned earlier

have been done in one-mass systems, either for linear or rotary

positioning systems. Since all the compensator parameters of

the NCTF controller are based on the NCT information, the

introduction of the PI with notch filter (NF) compensator are

adopted in this modification because the object response is

vibrates due to mechanical resonance of the plant. Thus, the

response will be unstable [23].

The effectiveness of the controller was examined with

experimental two-mass rotary positioning system as shown in

Fig. 10. Its structure consists of an NCT and a PI with NF as a

compensator. The positioning performances and robustness of

the controller due to inertia and friction variations have been

evaluated and compared with PID controllers. Further improve

of NCTF controller to overcome the problem of integrator

windup due to saturation problem also has been done by

author [24]. The improved NCTF controller is evaluated

experimentally using rotary two-mass positioning system. It

has been shown that the N.TF controller is effective for

positioning system and much more robust to inertia and

friction variations then the PID controllers [25].

The intelligent based approach also had been used to

improve the performance of the NCTF controller with PI

compensator. In [26], the NCTF with extended minimal

resource allocation algorithm (EMRAN) as a compensator is

introduced for two-mass rotary PTP positioning systems. The

effectiveness of the NCTF-EMRAN controller is examined by

simulation and it showed that the NCTF-EMRAN controller

has a better positioning performance than the existed NCTF

controller. The simulation results also proved that proposed

controller is much more robust than the conventional NCTF

controller due to load variations for two-mass rotary PTP

positioning systems.

Figure 10. Lab-scale two-mass rotary systems

TABLE I

NCTF CONTROL RESEARCH SUMMARY

Approach PTP

Positioning

System

Object

Rotary Positioning Linear Positioning

Classical approach

One-mass

system

Initial proposed

(Wahyudi, 2002)

Jury’s test for

stability region

(Wahyudi et al., 2003)

Mechanism with microdynamic

characteristic (Sato et

al., 2004) Non-friction

mechanism with PI

compensator (Chong and Sato, 2008)

Etc.

Two-mass system

PI with NF (Fitri et. al, 2009)

PI+NF with Anti-

windup scheme (Fitri and Rini, 2010)

PI with conditional

notch filter (Sato and

Maeda, 2008)

Intelligent-

system-based

approach

One-mass

system

Fuzzy-based initial proposed (Wahyudi et

al., 2005)

Fuzzy anti-windup scheme (Wahyudi et

al., 2007)

Double mode (Wahyudi and

Purtojo, 2007)

Modified fuzzy

membership and rule

base (Purtojo et al.,2008)

Reduced structure

(Purtojo et. al, 2009)Etc

Two-mass

system

EMRAN (Fitri and

Andika, 2011) n/a

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 1949

V. SUMMARY

Precision positioning systems are mainly used in industrial

machines applications such as machine tools, measuring

machines and semiconductor manufacturing systems. The

performances of the machines depend on the positioning and

accuracy of the systems. The literatures review of various

NCTF controller schemes for PTP positioning systems either

in one-mass or multi-mass system has been presented. The

NCTF control system concept also has been discussed. The

NCTF control system is relatively a new practical control

design for positioning system. Its structure consists of an NCT

and a compensator. The NCT construction remains simple

since it was firstly proposed since 2002.

The PI compensator of NCTF controller depends on the

selection of natural frequency and damping ratio in the stable

region to compute the gains. The stable region can be defined

theoretically or experimentally. The design process is

straightforward, fast and easy However, the stable region

remains a trial and error process due to unlimited possible

combinations.

The intelligent-based compensator for the NCTF controller

had been introduced in order to eliminate the trial and error

process. An NCTF controller with fuzzy compensator shows it

effectiveness in design process and its performance to replace

PI compensator. However, some problems related to its

structure, selection of membership function and it rules are still

open. Most of the NCTF controller schemes had been applied

to one-mass positioning system. The NCTF controller with

intelligent-based compensator has not been observed for CP

control systems.

ACKNOWLEDGMENT

This research is supported by Malaysia-Japan International

Institute of Technology (MJIIT), Universiti Teknologi

Malaysia International Campus Kuala Lumpur.

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1950 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)