# Experimental Evaluation of Novel Master-Slave Configurations for Position Control under Random Network Delay and Variable Load for Teleoperation

Authors: Ahmet Kuzu; Seta Bogosyan; Metin Gokasan; Asif Sabanovic
Journal: Mathematical Problems in Engineering
 (2014)

---

## Abstract

This paper proposes two novel master-slave configurations that provide improvements in both control and communication aspects of teleoperation systems to achieve an overall improved performance in position control. The proposed novel master-slave configurations integrate modular control and communication approaches, consisting of a delay regulator to address problems related to variable network delay common to such systems, and a model tracking control that runs on the slave side for the compensation of uncertainties and model mismatch on the slave side. One of the configurations uses a sliding mode observer and the other one uses a modified Smith predictor scheme on the master side to ensure position transparency between the master and slave, while reference tracking of the slave is ensured by a proportional-differentiator type controller in both configurations. Experiments conducted for the networked position control of a single-link arm under system uncertainties and randomly varying network delays demonstrate significant performance improvements with both configurations over the past literature.


---

## Body

## 1. Introduction

Teleoperation and bilateral control systems have been attracting significant interest due to their potential to contribute to human life, that is, teleoperated robots that contribute to safety and security in hazardous environments or exploration in remote areas or medical robots that can perform telesurgery [1]. Irrespective of the application, bilateral control is faced, to some extent, with problems resulting from uncertainties on the slave side and unpredictable network delays, which becomes significant when the Internet is used as the communication media.Numerous studies have been performed for time delay compensation in bilateral control systems. The scattering variables approach [2] is a passivity based approach, using transmission line theories. In this approach, the data transfer between systems is designed in a way to avoid losses, hence ensuring passivity. The method has been initially designed for constant delay and further extended to variable delay. However, although stability is guaranteed according to the passivity theory, no transparency analysis is provided with the scattering variables method. The wave variables method in [3] is also derived from the scattering variables theory, based on the addition of a damping term to ensure stability in terms of passivity. However, in this method, transparency and stability are conflicting performance parameters. This issue is often addressed by the adaptive tuning of damping.Optimal control methods have also been implemented to bilateral control with an aim to compensate for time delay while seeking an optimal solution for the stability and performance requirements of the system [4, 5]. Among other studies in the area, one can mention [6] with 2 types of PD controllers, [5] using L2 stability, [7] using multirate sampling, [8] on transparency and contact stability for single-master, multiple-slave telemanipulation, and [9] for the master- slave control of a multifingered humanoid by feeling the finger-tip force. There are also neural network based teleoperation studies as in [10, 11].There are also sliding-mode control (SMC) approaches as in [12, 13]. The SMC based studies often consider the delay effects as a disturbance, hence seeking ways to make the system robust to such disturbances via control. In the field of medicine, for example, there is active research on time-delay compensation using SMC framework [14]. Other examples are [15], which uses SMC as a base for developing an efficient and robust adaptive fuzzy controller; in [16], equivalent control based SMC is used mainly for control delay compensation; in [17] the master control is performed via an impedance controller and the slave control via SMC controller. A recent study has proposed an SMC framework to simplify the interpretation of tasks in a multibody mechanical system, applicable to bilateral and multilateral control [18]. Sliding-mode control (SMC) based approaches in bilateral control often consider the delay effects as a disturbance, hence seeking ways to make the system robust to such disturbances via control. The well-known chattering problem associated with SMC systems can only be reduced with very high switching frequencies, which naturally conflicts with the conditions of time delay systems. To address this issue, chattering-free SMCs are proposed, but the high gain requirement of such systems is a major cause for instability under time delay conditions, yielding an acceptable performance mostly under short time delay (shorter than the sampling interval).Smith predictor (SP) based applications mentioned above perform time delay compensation by using the system model and time delay model. The standard Smith predictor [19] will provide a good performance under known model and delay conditions, but will perform very poorly under random network delay, model, and load uncertainties, inherent to bilateral control systems. Astrom’s Smith predictor [20] is proposed to improve SP’s performance to some extent in the face of uncertainties; however, for an acceptable performance in bilateral control applications like the one under consideration, additional measures should be taken for delay regulation and disturbance rejection.A more recent approach in bilateral control is the consideration of the communication delay effect as a disturbance, which is further addressed by the design of an observer, namely, a communication delay observer (CDOB). The method is shown to be more effective than the Smith predictor approach due to its independence of modeling errors and capability to handle variable delays as normally expected with the Internet. Moreover this method is as applicable to a SISO system as it is to MIMO systems [21, 22]. The CDOB approach lumps the delays in the control and measurement loop and proposes a 1st-order observer derived under the assumption of a linear system. The approach is based on the empirical determination of the cutoff, g, and, more recently, of the time constant, T. Although performing well under constant delay, the authors mention ongoing problems in practical applications under variable time delay and slave uncertainties.This paper builds on the disturbance observer approach [12, 13] taken for the solution of network delays in bilateral control and aims to address specifically the variable delay, variable load, and model mismatch problems of [12, 13].The main contribution of this study is developing and practically implementing two novel master-slave system configurations that yield a significantly improved performance in position control. Each configuration consists of a delay regulator integrated with disturbance rejection schemes on both master and slave sides. More specifically, the following two configurations are developed and tested under variable network delay and the model mismatch problems of bilateral control systems: (1) sliding mode observer (SMO) to compensate for measurement delay on the master side and a model tracking controller (MTC) on the slave side to reduce the effects of load uncertainties and model mismatch between master and slave; (2) Astrom’s Smith predictor (ASP) to compensate for the effects of network delay on the master side and MTC against slave side uncertainties. Both configurations use the same delay regulator approach [23], which contributes significantly to the disturbance rejection performances of the SMO and ASP, as will be demonstrated with experimental results.The proposed observer-regulator-controller configurations are tested for step type and bidirectional type load and reference trajectories under random network delays. Throughout the experiments, the emulated random delay is varied between 100 and 400 milliseconds, based on the network delay measured in [24], for a networking implementation between country-region France and place country-region USA using UDP/IP Internet protocol.The organization of the paper is as follows. Section2 presents the problem focused on. Sections 3, 4, and 5 discuss the functional blocks used in proposed topologies, delay regulator, estimation schemes, and model tracking control consequently. Section 6 shows their experimental results, with conclusions and future directions in Section 7.


## 2. System Configuration

The general configuration of the master-slave system considered in this study is given in Figure1.Figure 1
Configuration of the bilateral control system with communication delays both in control and feedback paths.In this master-slave configuration, the human operator forces the master manipulator, which is in compliance mode, and generates a reference trajectory on the master side. This reference trajectory, together with the trajectory data coming from the slave side through the Internet, is considered by the master controller in the generation of the control signal that is generated to be sent to the slave side. On the slave side, the control signal coming from the master side through the Internet and the actual slave trajectory data is processed by the slave controller and actual control signal is generated. The information sent from the master side to the slave side is a message package containing the tapped control input signal (the reference current value) and a sequence ID. On slave side, more specifically, on the received side of the slave regulator, this information is processed to get the actual current input signal to be applied as reference to the slave side. As a result of this process, the input current signal is now compensated for data losses and the delay is regulated to a constant value.The equation of motion for a direct-drive single link arm with load can be given as follows:(1)
θ
˙
t
=
ω
t
,
(2)
ω
˙
t
=
K
t
J
u
t
-
B
J
ω
t
-
T
L
J
,
where K
t is torque constant (N-m
/
A), J is system inertia (kg-
m
2), B is viscous friction (N-ms
/
rad), u
=
i
q is control current (A), and T
L is the gravitational load.


## 3. Design of Delay Regulator

For bilateral control systems using the Internet as the communication medium, it is necessary to consider the delay characteristics of different Internet protocols. Currently, the more commonly used IPs (Internet protocols) are the transport control protocol (TCP/IP) and the user datagram protocol (UDP). TCP provides a point-to-point channel for applications that require reliable communication. It is a higher-level protocol that manages to robustly string together data packets, sorting them and retransmitting them as necessary to reliably retransmit data. Further, TCP/IP is confirmation based; that is, it transmits data and waits for confirmation from the other side. If not fulfilled, it retransmits the data. With TCP/IP, there is no data loss.The UDP protocol does not guarantee communication between two applications on the network. While TCP/IP is connection based, UDP is just a simple serial communication channel. Much like sending a letter through mail, and unlike TCP/IP, UDP does not confirm arrival, hence eliminating data retransmission. On the other hand, while its faster transmission rate may make UDP more preferable for most real-time control applications, some delay regulation measure is also necessary to minimize the data loss.The delay regulator works are based on the following principle: each transmitted UDP packet consists of the current plus31 previous data samples, in addition to a sequence ID. Once transmitted to the slave side, this packet is stored into a memory cell identified by the packet’s sequence ID. The number of stored packets on the receiving end is limited with the buffer size, N. During the very first send-receive process, stored packets are not fed to the related control process (to master for feedback or to slave for control) until a selected L
<
N threshold is reached. This L
/
T value determines the selected regulation period, which when exceeded, the first data, x
(
k
), is fed to related control process, and this memory cell is labelled as null
(
⌀
). In the next sample time x
k
+
1 will be fed to the control process until we face a data loss, in which case x
k
+
2 will be null. In this case the algorithm checks the next memory cell and then the next one until a noncorrupted x
k
+
2 value is founded in the memory cells below [23, 25]. The figure of a sample signal flow is seen in Figure 2.Figure 2
Delay regulator sample signal flow diagram.


## 4. Design of Control and Estimation Schemes for the Master-Slave System

Two control approaches are developed for the master side: one based on Smith predictor principles and one using sliding mode concepts. A discussion of both will be provided in this section.


### 4.1. Astrom’s Smith Predictor on Master Side

The Smith predictor (SP) concept [19] is based on the design of a controller that can predict how the effects of system changes will affect the controlled variable (system output) in the future. The standard SP configuration, which requires the time delay to be constant (or known), has the shortcoming of poor disturbance rejection. Watanabe’ Smith predictor (WSP) [26] and Astrom’s Smith predictor (ASP) [20], given in Figure 3, have been proposed to overcome this problem. While both ASP and WSP are two degree of freedom modified Smith predictors, here we prefer Astrom’s Smith predictor because, contrary to Watanabe’s Smith predictor, effect of auxiliary controller does not degrade main controller performance [20].Figure 3
Astrom’s Smith predictor.Astrom’s Smith predictor (ASP) decouples the disturbance response from the reference response, allowing the two to be independently optimized. Furthermore, its structure provides the designer with more freedom to choose the transfer function,M
asp
(
s
). Considering the developed delay regulator and the slave-side disturbance rejection scheme (to be discussed in the next section), an ASP based master control appears to be well suited for the targeted performance standards in this study. Within this configuration, the human operator generates the master trajectory, which then leads to the generation of the control input current to be transmitted to the slave side as explained in Section 2. At the slave side, the delayed control signal coming from the master side (through the Internet) and the actual slave feedback data are processed by the slave controller and the actual control signal is generated and applied to the slave. The ASP is expected to compensate for disturbances caused by communication discrepancies between master and slave, when the buffer side is exceeded. Figure 3 presents the designed ASP within the proposed master-slave.For the determination of the transfer function,M
asp
(
s
) of the ASP, the reference-to-output and disturbance-to-output transfer functions should first be taken into consideration for the system. With the given structure and with the assumption that the delay is constant, L, the reference-to-output transfer function will be independent of M
asp
(
s
) [27, 28]:
(3)
θ
slvmdl
(
s
)
θ
refmst
(
s
)
=
C
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
C
asp
(
s
)
P
model
(
s
)
×
1
+
M
asp
s
P
model
s
e
-
s
L
1
+
M
asp
s
P
model
s
e
-
s
L
,
θ
slvmdl
(
s
)
θ
refmst
(
s
)
=
C
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
C
asp
(
s
)
P
model
(
s
)
.HereC
asp is the main controller whose parameters are designed by ignoring network delay. In this work we choose C
asp as a PID controller whose parameters are k
PCasp, k
ICasp, and k
DCasp.On the other hand, the disturbance response is as follows:(4)
θ
slvmdl
(
s
)
d
ntw
(
s
)
=
P
model
(
s
)
e
-
s
L
1
+
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
,
where
(5)
P
model
s
=
K
t
n
s
J
n
s
+
B
n
.AlsoK
t
n, J
n, and B
n are the rated parameter values of K
t, J, and B, respectively.To suppress the disturbanced
^
ntw should track d
ntw in Figure 3. The transfer function from d
ntw to d
^
ntw is
(6)
d
^
ntw
(
s
)
d
ntw
(
s
)
=
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
.Then(7)
M
asp
s
=
k
PMasp
+
s
k
DMasp
.Here loop transfer function is(8)
G
l
s
=
M
asp
s
P
model
s
e
-
s
L
,
G
l
(
s
)
=
k
PMasp
+
s
k
DMasp
K
t
n
s
(
J
n
s
+
B
n
)
e
-
s
L
if we rearrange the equations
(9)
G
l
(
s
)
=
k
PMasp
+
s
k
DMasp
s
K
t
n
(
J
n
s
+
B
n
)
e
-
s
L
and define
(10)
M
asp
′
s
=
k
PMasp
+
s
k
DMasp
(
s
)
s
=
k
PMasp
′
+
k
IMasp
′
s
,
P
model
′
s
=
K
t
n
J
n
s
+
B
n
e
-
s
L
,
where k
IMasp
′
=
k
PMasp and k
PMasp
′
=
k
DMasp.Due to the PD-PI relation above, it is possible to design a PD controller for the position control problem under consideration, using the guidelines of the PI design in [29] given based on the system’s sensitivity requirements dictated by N
s and derived for a velocity control system, different from our position control system:
(11)
k
DMasp
=
1
L
1.451
-
1.508
N
s
J
n
K
t
n
,
k
PMasp
=
1
L
1.451
-
1.508
N
s
B
n
K
t
n
.Here,N
s is determined by the desired sensitivity specification and is defined as
(12)
N
s
=
max
⁡
0
≤
ω
<
∞
1
L
1
1
+
P
model
(
j
ω
)
M
(
j
ω
)
.N
s can also be defined as the inverse of the shortest distance of the open loop transfer function from the Nyquist curve as seen in Figure 4. The major advantages of N
s are that by selecting N
s, performance factors
(13)
A
m
>
N
s
N
s
-
1
φ
m
>
2
arcsin
1
2
N
s
can be constructed. Here, A
m denotes gain margin and φ denotes phase margin.Figure 4
Nyquist diagram of loop function.Reasonable values of theN
s are in the range of 1.3 to 2.Alternatively, Ziegler-Nichols [30] and Astrom-Hagglund [31] methods can also be used for the design of the M
asp
(
s
) controller.


### 4.2.  Design of Sliding Mode Observer on Master Side

The developed sliding mode observer (SMO) aims to estimate the actual slave position and velocity in the face of the network delay encountered in the feedback loop. This delay is now constant with the use of the delay regulator, which is demonstrated to significantly improve the performance of the SMO compared to past studies of the authors, together with the use of the proposed model following controller. The observer (on the master side) takes into account the following slave model, the outputs of which are fed to the master as slave feedback with the assumption that the actual slave system will track the model closely with the designed MTC.The model of the slave plant is(14)
θ
˙
slvmdl
t
=
ω
slvmdl
t
,
ω
˙
slvmdl
t
=
K
t
n
J
n
u
slv
t
-
B
n
J
n
ω
slvmdl
t
.The master side observer designed for the slave has the following form:(15)
θ
˙
e
(
t
)
=
ω
e
(
t
)
ω
˙
e
t
=
K
t
n
J
n
u
slv
t
-
B
n
J
n
ω
e
t
+
u
o
t
.X
=
[
θ
e
ω
e
]
T are observer states. u
o is control input of the observer (to be determined based on SM theory).Slave states measured on the master side which is the output of delay regulator areθ
dlyregout, ω
dlyregout:
(16)
θ
dlyregout
k
T
=
θ
slvmdl
k
T
-
L
,
ω
dlyregout
k
T
=
ω
slvmdl
k
T
-
L
,
where L is the regulated delay.The control input applied to the slave also deviates from the actual control input by the same delay as(17)
u
slv
k
T
=
u
mst
k
T
-
L
.Next, for the design of the observer, the sliding manifold is selected as(18)
σ
t
=
c
smo
e
smo
t
+
e
˙
smo
t
,
where e
smo
(
t
) and e
˙
smo
(
t
) are as follows:
(19)
e
smo
t
=
θ
dlyregout
t
-
θ
e
t
-
L
,
e
˙
smo
t
=
ω
dlyregout
t
-
ω
e
t
-
L
.With a properly selected Lyapunov candidate, a control will be designed for the SM based observer that will force the observed states,θ
e
(
k
T
-
L
) and ω
e
(
k
T
-
L
), to the measured θ
dlyregout, ω
dlyregout. As given in (16), this actually indicates that the actual slave state values (before the delay) have been reached for use in the master controller.The Lyapunov candidate and its derivative are selected as follows to satisfy the following conditions:(20)
V
t
=
σ
2
t
,
(21)
V
˙
t
=
σ
t
σ
˙
t
=
-
d
smo
σ
2
t
,
where
(22)
σ
˙
t
=
c
smo
e
˙
smo
t
+
ω
˙
dlyregout
t
-
ω
˙
e
t
-
L
.Equations (21) and (22) are used to derive the SM control law as follows [12]:
(23)
σ
˙
t
=
-
d
smo
σ
t
.By substituting (14), (15), and (18) into (22),
(24)
σ
˙
t
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
-
K
t
n
J
n
u
mst
t
-
L
+
B
n
J
n
ω
e
t
-
L
-
u
o
t
.Next, we define(25)
u
o
(
t
)
eq
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
(
t
-
L
)
-
K
t
n
J
n
u
mst
(
t
-
L
)
which converts (24) into
(26)
σ
˙
t
=
u
o
t
eq
-
u
o
t
.Ifu
o
(
t
)
=
[
u
o
(
t
)
]
eq, then σ
˙
=
0, and per (23), σ
=
0.To calculate the observer control, we discretizeσ
˙ under the assumption of a very high sampling rate; hence, (26) becomes
(27)
u
o
(
k
T
-
T
)
-
u
o
k
T
-
T
eq
=
σ
(
k
T
)
-
σ
(
k
T
-
T
)
T
and also
(28)
u
0
k
T
-
u
o
k
T
eq
=
-
d
smo
σ
k
T
.Assuming that[
u
o
(
k
)
]
eq does not change between two sampling periods,
(29)
u
o
k
T
eq
=
u
o
k
T
-
T
eq
.By rearranging (28) and subtracting from (27) we get
(30)
u
o
k
=
u
o
k
-
1
+
1
+
d
smo
T
σ
k
-
σ
k
-
1
T
.The control in (30) will enforce the sliding mode to the selected manifold. With the application of this control, and with the consideration of
(31)
u
o
(
t
)
eq
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
t
-
L
-
K
t
n
J
n
u
mst
t
-
L
.
The observer system in (15) can be rewritten as
(32)
θ
˙
e
t
-
L
=
ω
e
t
-
L
,
ω
˙
e
t
-
L
=
-
B
n
J
n
ω
e
(
t
-
L
)
+
K
t
n
J
n
u
mst
(
t
-
L
)
+
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
t
-
L
-
K
t
n
J
n
u
mst
t
-
L
,which yields(33)
ω
˙
dlyregout
(
t
)
-
ω
˙
e
(
t
-
L
)
︸
e
¨
smo
(
t
)
+
c
smo
e
˙
smo
(
t
)
=
0
.Inspecting (23), it can be said that when σ
˙
(
t
)
→
0
σ
(
t
)
→
0. This indicates that e
˙
smo
(
t
)
→
0, c
smo
e
smo
(
t
)
→
0; that is,
(34)
ω
e
t
-
L
=
ω
dlyregout
t
=
ω
slvmdl
t
-
L
,
θ
e
t
-
L
=
θ
dlyregout
t
=
θ
slvmdl
t
-
L
.Block diagram of described Sliding Mode Observer is seen in Figure5.Figure 5
Diagram of sliding mode observer.


## 4.1. Astrom’s Smith Predictor on Master Side

The Smith predictor (SP) concept [19] is based on the design of a controller that can predict how the effects of system changes will affect the controlled variable (system output) in the future. The standard SP configuration, which requires the time delay to be constant (or known), has the shortcoming of poor disturbance rejection. Watanabe’ Smith predictor (WSP) [26] and Astrom’s Smith predictor (ASP) [20], given in Figure 3, have been proposed to overcome this problem. While both ASP and WSP are two degree of freedom modified Smith predictors, here we prefer Astrom’s Smith predictor because, contrary to Watanabe’s Smith predictor, effect of auxiliary controller does not degrade main controller performance [20].Figure 3
Astrom’s Smith predictor.Astrom’s Smith predictor (ASP) decouples the disturbance response from the reference response, allowing the two to be independently optimized. Furthermore, its structure provides the designer with more freedom to choose the transfer function,M
asp
(
s
). Considering the developed delay regulator and the slave-side disturbance rejection scheme (to be discussed in the next section), an ASP based master control appears to be well suited for the targeted performance standards in this study. Within this configuration, the human operator generates the master trajectory, which then leads to the generation of the control input current to be transmitted to the slave side as explained in Section 2. At the slave side, the delayed control signal coming from the master side (through the Internet) and the actual slave feedback data are processed by the slave controller and the actual control signal is generated and applied to the slave. The ASP is expected to compensate for disturbances caused by communication discrepancies between master and slave, when the buffer side is exceeded. Figure 3 presents the designed ASP within the proposed master-slave.For the determination of the transfer function,M
asp
(
s
) of the ASP, the reference-to-output and disturbance-to-output transfer functions should first be taken into consideration for the system. With the given structure and with the assumption that the delay is constant, L, the reference-to-output transfer function will be independent of M
asp
(
s
) [27, 28]:
(3)
θ
slvmdl
(
s
)
θ
refmst
(
s
)
=
C
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
C
asp
(
s
)
P
model
(
s
)
×
1
+
M
asp
s
P
model
s
e
-
s
L
1
+
M
asp
s
P
model
s
e
-
s
L
,
θ
slvmdl
(
s
)
θ
refmst
(
s
)
=
C
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
C
asp
(
s
)
P
model
(
s
)
.HereC
asp is the main controller whose parameters are designed by ignoring network delay. In this work we choose C
asp as a PID controller whose parameters are k
PCasp, k
ICasp, and k
DCasp.On the other hand, the disturbance response is as follows:(4)
θ
slvmdl
(
s
)
d
ntw
(
s
)
=
P
model
(
s
)
e
-
s
L
1
+
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
,
where
(5)
P
model
s
=
K
t
n
s
J
n
s
+
B
n
.AlsoK
t
n, J
n, and B
n are the rated parameter values of K
t, J, and B, respectively.To suppress the disturbanced
^
ntw should track d
ntw in Figure 3. The transfer function from d
ntw to d
^
ntw is
(6)
d
^
ntw
(
s
)
d
ntw
(
s
)
=
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
1
+
M
asp
(
s
)
P
model
(
s
)
e
-
s
L
.Then(7)
M
asp
s
=
k
PMasp
+
s
k
DMasp
.Here loop transfer function is(8)
G
l
s
=
M
asp
s
P
model
s
e
-
s
L
,
G
l
(
s
)
=
k
PMasp
+
s
k
DMasp
K
t
n
s
(
J
n
s
+
B
n
)
e
-
s
L
if we rearrange the equations
(9)
G
l
(
s
)
=
k
PMasp
+
s
k
DMasp
s
K
t
n
(
J
n
s
+
B
n
)
e
-
s
L
and define
(10)
M
asp
′
s
=
k
PMasp
+
s
k
DMasp
(
s
)
s
=
k
PMasp
′
+
k
IMasp
′
s
,
P
model
′
s
=
K
t
n
J
n
s
+
B
n
e
-
s
L
,
where k
IMasp
′
=
k
PMasp and k
PMasp
′
=
k
DMasp.Due to the PD-PI relation above, it is possible to design a PD controller for the position control problem under consideration, using the guidelines of the PI design in [29] given based on the system’s sensitivity requirements dictated by N
s and derived for a velocity control system, different from our position control system:
(11)
k
DMasp
=
1
L
1.451
-
1.508
N
s
J
n
K
t
n
,
k
PMasp
=
1
L
1.451
-
1.508
N
s
B
n
K
t
n
.Here,N
s is determined by the desired sensitivity specification and is defined as
(12)
N
s
=
max
⁡
0
≤
ω
<
∞
1
L
1
1
+
P
model
(
j
ω
)
M
(
j
ω
)
.N
s can also be defined as the inverse of the shortest distance of the open loop transfer function from the Nyquist curve as seen in Figure 4. The major advantages of N
s are that by selecting N
s, performance factors
(13)
A
m
>
N
s
N
s
-
1
φ
m
>
2
arcsin
1
2
N
s
can be constructed. Here, A
m denotes gain margin and φ denotes phase margin.Figure 4
Nyquist diagram of loop function.Reasonable values of theN
s are in the range of 1.3 to 2.Alternatively, Ziegler-Nichols [30] and Astrom-Hagglund [31] methods can also be used for the design of the M
asp
(
s
) controller.


## 4.2.  Design of Sliding Mode Observer on Master Side

The developed sliding mode observer (SMO) aims to estimate the actual slave position and velocity in the face of the network delay encountered in the feedback loop. This delay is now constant with the use of the delay regulator, which is demonstrated to significantly improve the performance of the SMO compared to past studies of the authors, together with the use of the proposed model following controller. The observer (on the master side) takes into account the following slave model, the outputs of which are fed to the master as slave feedback with the assumption that the actual slave system will track the model closely with the designed MTC.The model of the slave plant is(14)
θ
˙
slvmdl
t
=
ω
slvmdl
t
,
ω
˙
slvmdl
t
=
K
t
n
J
n
u
slv
t
-
B
n
J
n
ω
slvmdl
t
.The master side observer designed for the slave has the following form:(15)
θ
˙
e
(
t
)
=
ω
e
(
t
)
ω
˙
e
t
=
K
t
n
J
n
u
slv
t
-
B
n
J
n
ω
e
t
+
u
o
t
.X
=
[
θ
e
ω
e
]
T are observer states. u
o is control input of the observer (to be determined based on SM theory).Slave states measured on the master side which is the output of delay regulator areθ
dlyregout, ω
dlyregout:
(16)
θ
dlyregout
k
T
=
θ
slvmdl
k
T
-
L
,
ω
dlyregout
k
T
=
ω
slvmdl
k
T
-
L
,
where L is the regulated delay.The control input applied to the slave also deviates from the actual control input by the same delay as(17)
u
slv
k
T
=
u
mst
k
T
-
L
.Next, for the design of the observer, the sliding manifold is selected as(18)
σ
t
=
c
smo
e
smo
t
+
e
˙
smo
t
,
where e
smo
(
t
) and e
˙
smo
(
t
) are as follows:
(19)
e
smo
t
=
θ
dlyregout
t
-
θ
e
t
-
L
,
e
˙
smo
t
=
ω
dlyregout
t
-
ω
e
t
-
L
.With a properly selected Lyapunov candidate, a control will be designed for the SM based observer that will force the observed states,θ
e
(
k
T
-
L
) and ω
e
(
k
T
-
L
), to the measured θ
dlyregout, ω
dlyregout. As given in (16), this actually indicates that the actual slave state values (before the delay) have been reached for use in the master controller.The Lyapunov candidate and its derivative are selected as follows to satisfy the following conditions:(20)
V
t
=
σ
2
t
,
(21)
V
˙
t
=
σ
t
σ
˙
t
=
-
d
smo
σ
2
t
,
where
(22)
σ
˙
t
=
c
smo
e
˙
smo
t
+
ω
˙
dlyregout
t
-
ω
˙
e
t
-
L
.Equations (21) and (22) are used to derive the SM control law as follows [12]:
(23)
σ
˙
t
=
-
d
smo
σ
t
.By substituting (14), (15), and (18) into (22),
(24)
σ
˙
t
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
-
K
t
n
J
n
u
mst
t
-
L
+
B
n
J
n
ω
e
t
-
L
-
u
o
t
.Next, we define(25)
u
o
(
t
)
eq
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
(
t
-
L
)
-
K
t
n
J
n
u
mst
(
t
-
L
)
which converts (24) into
(26)
σ
˙
t
=
u
o
t
eq
-
u
o
t
.Ifu
o
(
t
)
=
[
u
o
(
t
)
]
eq, then σ
˙
=
0, and per (23), σ
=
0.To calculate the observer control, we discretizeσ
˙ under the assumption of a very high sampling rate; hence, (26) becomes
(27)
u
o
(
k
T
-
T
)
-
u
o
k
T
-
T
eq
=
σ
(
k
T
)
-
σ
(
k
T
-
T
)
T
and also
(28)
u
0
k
T
-
u
o
k
T
eq
=
-
d
smo
σ
k
T
.Assuming that[
u
o
(
k
)
]
eq does not change between two sampling periods,
(29)
u
o
k
T
eq
=
u
o
k
T
-
T
eq
.By rearranging (28) and subtracting from (27) we get
(30)
u
o
k
=
u
o
k
-
1
+
1
+
d
smo
T
σ
k
-
σ
k
-
1
T
.The control in (30) will enforce the sliding mode to the selected manifold. With the application of this control, and with the consideration of
(31)
u
o
(
t
)
eq
=
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
t
-
L
-
K
t
n
J
n
u
mst
t
-
L
.
The observer system in (15) can be rewritten as
(32)
θ
˙
e
t
-
L
=
ω
e
t
-
L
,
ω
˙
e
t
-
L
=
-
B
n
J
n
ω
e
(
t
-
L
)
+
K
t
n
J
n
u
mst
(
t
-
L
)
+
c
smo
e
˙
smo
(
t
)
+
ω
˙
dlyregout
(
t
)
+
B
n
J
n
ω
e
t
-
L
-
K
t
n
J
n
u
mst
t
-
L
,which yields(33)
ω
˙
dlyregout
(
t
)
-
ω
˙
e
(
t
-
L
)
︸
e
¨
smo
(
t
)
+
c
smo
e
˙
smo
(
t
)
=
0
.Inspecting (23), it can be said that when σ
˙
(
t
)
→
0
σ
(
t
)
→
0. This indicates that e
˙
smo
(
t
)
→
0, c
smo
e
smo
(
t
)
→
0; that is,
(34)
ω
e
t
-
L
=
ω
dlyregout
t
=
ω
slvmdl
t
-
L
,
θ
e
t
-
L
=
θ
dlyregout
t
=
θ
slvmdl
t
-
L
.Block diagram of described Sliding Mode Observer is seen in Figure5.Figure 5
Diagram of sliding mode observer.


## 5. Design of Model Tracking Control Scheme on Slave Side

In this section, the design of the proposed model tracking control (MTC) is discussed. The MTC based slave control system forces the actual slave system to track a desired slave model, hence achieving disturbance rejection in the face of parameter and load uncertainties. This model tracking scheme is represented in Figure6 [32, 33]. It should be noted that the slave feedback used on the master side is the output of the slave “model,” not the output of the actual slave. Integrated master-slave system is the output of the model system. The use of this model on both master and slave sides is an approach taken in this study that significantly improves master-slave tracking performance. With this approach, the master and slave controllers can also be designed separately.Figure 6
Architecture of model tracking control at slave side.To derive the model tracking controller,C
mtc
(
s
), the mathematical model of the actual plant, P
slv
(
s
), in (2) is taken into consideration in the following form:
(35)
K
t
J
u
slv
+
u
aux
-
T
L
J
-
B
J
ω
slvact
=
ω
˙
slvact
,
where T
L is load torque [
Nm
], J is total moment of inertia [
kg
m
2
], B is total viscous friction coefficient [
Nm
s
/
rd
⁡
], w
slvact is angular velocity [
rd
⁡
/
s
], K
t is torque constant [
Nm
/
A
], u
slv is control input to track the known part of the slave model, and u
aux is control input to compensate for slave model uncertainties.The model below represents the known portion of the slave model:(36)
K
t
n
J
n
u
slv
-
B
n
J
n
ω
slvmdl
=
ω
˙
slvmdl
,
where all values reflect the known slave model parameters and variables, as below:J
n is moment of inertia of slave model [
kg
m
2
];
B
n is viscous friction coefficient of slave model [
Nm
s
/
rd
⁡
];
ω
slvmdl is angular velocity [
rd
⁡
/
s
];
K
t
n is torque constant [
Nm
/
A
].With the aim of deriving the appropriate tracking controller,C
mtc, first the error between the actual plant and model plant outputs should be defined as
(37)
e
mtc
=
θ
slvact
-
θ
slvmdl
,
e
˙
mtc
=
ω
slvact
-
ω
slvmdl
,
e
¨
mtc
=
ω
˙
slvact
-
ω
˙
slvmdl
.Using (35) and (36), the second derivative of the error is defined as
(38)
e
¨
mtc
=
-
K
t
n
J
n
u
slv
+
B
n
J
n
ω
slvmdl
+
K
t
J
u
slv
+
u
aux
-
T
L
J
-
B
J
ω
slvact
.Defining the error between actual and model parameter values with the symbol Δ as(39)
k
t
J
=
k
t
n
J
n
+
Δ
k
t
J
B
J
=
B
n
J
n
+
Δ
B
J
can be reorganized as below:
(40)
e
¨
mtc
=
K
t
n
J
n
-
u
slv
+
u
slv
+
u
aux
+
Δ
K
t
J
u
slv
+
u
aux
-
B
n
J
n
e
˙
mtc
-
Δ
B
J
ω
slvact
-
T
L
J
,
(41)
e
¨
mtc
+
B
n
J
n
e
˙
mtc
=
K
t
n
J
n
u
aux
-
T
L
J
+
Δ
K
t
J
u
slv
+
u
aux
-
Δ
B
J
ω
slvact
.Next, the load and parameter uncertainties are defined asd
mtc
(42)
1
J
n
d
mtc
≜
T
L
J
-
Δ
K
t
J
u
slv
+
u
aux
+
Δ
B
J
ω
slvact
.Here disturbance upper bound can also be defined as(43)
d
mtc
max
⁡
=
J
n
T
L
max
⁡
J
min
⁡
-
J
n
Δ
K
t
J
max
⁡
u
mtc
max
⁡
+
J
n
Δ
B
J
max
⁡
ω
slvact
max
⁡
.Equation (42) when substituted in (41) will yield the following error dynamics:
(44)
e
¨
mtc
+
B
n
J
n
e
˙
=
1
J
n
K
t
n
u
aux
-
d
mtc
.Inspecting (44), it could be observed that when
(45)
u
aux
⟶
d
mtc
K
t
n
,
e
˙
mtc
⟶
0
while
e
mtc
⟶
constant
.Fore
mtc
→
0, the following error dynamics should be derived:
(46)
e
¨
mtc
+
B
n
J
n
e
˙
mtc
+
k
mtc
e
mtc
=
0
.This condition requires the following term:(47)
1
J
n
K
t
n
u
aux
-
d
mtc
=
-
k
mtc
e
mtc
which results in the following relationships:
(48)
d
mtc
=
k
t
n
u
aux
+
k
mtc
J
n
e
mtc
,
(49)
u
aux
=
d
mtc
-
k
mtc
J
n
e
mtc
K
t
n
.Define a new variablez as
(50)
z
≜
d
mtc
-
k
mtc
J
n
e
⟶
d
=
z
+
k
mtc
J
n
e
mtc
.Assume thatd
mtc has a very slow variation:
(51)
z
˙
=
-
k
mtc
J
n
e
˙
mtc
z
¨
=
-
k
mtc
J
n
e
¨
mtc
.Rewrite (44) in terms of z:
(52)
z
¨
+
B
n
J
n
z
˙
+
k
mtc
z
=
k
mtc
d
mtc
.Hence(53)
z
¨
+
B
n
J
n
z
˙
+
k
mtc
z
=
k
mtc
k
mtc
J
n
e
mtc
+
K
t
n
u
aux
.To deriveC
mtc
(
s
), z in (53) is expressed in s-domain:
(54)
z
s
=
k
mtc
s
2
+
(
B
n
/
J
n
)
s
+
k
mtc
k
mtc
J
n
e
mtc
+
K
t
n
u
aux
which is substituted in d
mtc expression, yielding
(55)
d
mtc
=
k
mtc
s
2
+
(
B
n
/
J
n
)
s
+
k
mtc
k
mtc
J
n
e
mtc
+
K
t
n
u
aux
+
k
mtc
J
n
e
mtc
.Replacingd
mtc with its definition in (48),
(56)
K
t
n
u
aux
=
k
mtc
s
2
+
(
B
n
/
J
n
)
s
+
k
mtc
k
mtc
J
n
e
mtc
+
K
t
n
u
aux
+
k
mtc
J
n
e
mtc
-
k
mtc
J
n
e
mtc
.Expressing (56) in terms of aux, the expression for the tracking control, C
mtc
(
s
), can be derived as follows:
(57)
s
2
+
B
n
J
n
s
+
k
mtc
K
t
n
u
aux
=
k
mtc
K
t
n
u
aux
+
k
mtc
J
n
k
mtc
e
mtc
,
u
aux
=
J
n
k
mtc
2
s
2
+
B
n
/
J
n
s
︸
C
mtc
s
e
mtc
s
.Here, the controller,C
mtc
(
s
), is configured as a compensator and its output is added onto the PD control generated, which is the constant time delayed version of the control signal generated on the master side.


## 6. Experimental Results with Proposed Methods for the Two Master-Slave Configurations

In this section, experimental results will be provided with the proposed schemes, which are presented as two configurations. The controller parameters arec
smo
=
0.0001, d
smo
=
0.001, k
PCasp
=
k
PCsmo
=
0.92, k
ICasp
=
K
ICsmo
=
0.1, k
DCasp
=
k
DCsmo
=
2, k
PMasp
=
.
03, k
DMasp
=
.
12, and k
mtc
=
200. Also Figure 7 presents the master-slave configuration based on the modified SP and MTC, abbreviated as SP-MTC for brevity, and Figure 8 presents the master-slave configuration based on the modified SMO and MTC. In both configurations, the developed model tracking controller (MTC) forces the slave to track the desired model, hence avoiding instability issues and increasing tracking accuracy despite parameter uncertainties and disturbances on the slave side. As demonstrated in Figure 2, the control input (a current signal) for the slave side is generated by the master side controller, which takes into consideration the reference trajectory and the slave feedback received from the model. This is an important contribution of this study, as in the previous studies of the authors [13]; it was demonstrated that the use of the actual slave plant feedback causes steady state error and drift in the slave performance.Figure 7
Modified SP and MTC based master-slave configuration.Figure 8
SMO and MTC based master-slave configuration.The experimental results are obtained under random network delays both in the feedback and control loops. For the proper operation of the SMO and ASP schemes, a delay regulator is designed on both master and the slave sides to regulate these random delays to a constant delay value of 400 ms. This value was obtained from the intercontinental network experiments presented in [23]. To further challenge the slave plant, the load disturbance on the slave and the reference trajectories are applied as sinusoidal functions and bidirectional trajectories, respectively, which sometimes gives rise to short spikes.A direct-drive motor driven single-link arm is used in the experiments, the parameters of which are listed in Table1. The delay is generated as a random signal varying between 100 and 400 milliseconds.Table 1
Experiment parameters.
Parameter name
Parameter value
Description
V
q
n
60 V
Motor nominal voltage
i
q
n
5 A
Motor nominal current
R
q
0.6 Ω
Motor phase windings resistance
L
q
0.005 H
Motor phase windings inductance
K
b
2.3 Vsec/rad
Back e.m.f. constant
T
e
n
10 Nm
Motor nominal torque
K
v
i
1 A/V
Motor driver gain
ω
n
4 πrad/sec
Motor nominal speed
T
e
m
15 Nm
Motor maximum torque
K
t
2 Nm/A
Torque constant
J
0.012 kg-m2
Effective inertia
B
0.207 Nms/rad
Effective viscous friction
T
L
10sin
⁡
⁡
ΘNm
Load torqueFigures9 and 10 represent the performance of the ASP and SMO based configurations, respectively, under no load on the slave. The figures demonstrate the delay effect in all cases. Inspecting the zoomed versions of the diagrams, one may note a slightly smoother performance of ASP based configuration.(a) Reference tracking performance of slave with the ASP based configuration under no load (delay effect displayed); (b) zoomed version of performance.
(a)
(b)(a) Reference tracking performance of slave with the SMO based configuration under no load (delay effect displayed); (b) zoomed version of performance.
(a)
(b)Figures11 and 12 represent the performance of the ASP and SMO based configurations, respectively, under a sinusoidal load variation on the slave side. The figures demonstrate the delay effect in all cases. While a slightly smoother performance is noted with ASP again, both configurations display similar performances in terms of tracking error.(a) Reference tracking performance of slave with the ASP based configuration under sinusoidal disturbance (delay effect displayed); (b) zoomed version of performance.
(a)
(b)(a) Reference tracking performance of slave with the SMO based configuration under sinusoidal load (delay effect displayed); (b) zoomed version of performance.
(a)
(b)


## 7. Conclusions and Future Directions

This study builds on the disturbance observer based approach in bilateral control and contributes to significant improvements in both control and communication issues faced with position control aspects of bilateral control systems. To this aim, two novel master-slave configurations are proposed: one based on a sliding-mode observer and model-tracking controller and the other based on Astrom’s Smith predictor on the master side. Both configurations benefit from a delay regulator, which regulates the random network delay into a constant delay. Both configurations also use a MTC designed for the slave side disturbance rejection and trajectory tracking.Experiments are conducted on a single-link arm system under variable gravitational effects and a randomly varied network delay of 100–400 ms that impacts both the feedback and control loop. While the ASP is a more capable version of the standard SP against disturbances stemming from network and slave uncertainties, the much reduced system uncertainties via the proposed combination of the delay regulator and MTC contribute significantly to the overall performance.The delay regulator and MTC have also benefited the SMO based configuration significantly, which has been shown to demonstrate a poor tracking performance under variable network and slave disturbances in the authors’ previous studies, while achieving perfect tracking under no load and constant network delay. Hence, both configurations demonstrate a significantly improved tracking performance against model-mismatch and randomly varying network delay (within 100–400 ms) and can handle feedback loop deteriorations arising from the limited buffer size of the delay regulator. However, currently neither of the configurations can handle network delays exceeding 400 ms in the control loop. This issue requires further attention and will be addressed in the authors’ future papers.



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*Source: 608208-2014-12-24.xml*