Output Tracking Control for Networked Systems: A ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 9, SEPTEMBER 2014

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Output Tracking Control for Networked Systems: A Model-Based Prediction Approach Zhong-Hua Pang, Member, IEEE, Guo-Ping Liu, Fellow, IEEE, Donghua Zhou, Senior Member, IEEE, and Maoyin Chen

Abstract—This paper studies the problem of output tracking for networked control systems with network-induced delay, packet disorder, and packet dropout. The round-trip time (RTT) delay is redefined to describe these communication constraints in a unified way. By including the output tracking error as an additional state, the output tracking problem is converted into the stabilization problem of an augmented system. Based on the observer of the original state increment and the feedback of the output tracking error, a model-based networked predictive output tracking control (NPOTC) scheme is proposed to actively compensate for the random RTT delay. The closed-loop stability is proved to be independent of the RTT delay, and the separation principle for the design of the observer-based state feedback controller is still held in the NPOTC system. A two-stage controller design procedure is presented, which not only guarantees the stability of the closed-loop NPOTC system but also achieves the same output tracking performance as that of the local control system for time-varying reference signals. Both numerical simulations and practical experiments on an Internet-based servo motor system illustrate the effectiveness of the proposed method. Index Terms—Experiments, networked control systems (NCSs), output tracking control, predictive control, round-trip time (RTT) delay, stability and performance analysis.

I. I NTRODUCTION

D

ISTINCT from conventional point-to-point control systems, called local control systems (LCSs), networked control systems (NCSs) have many valuable advantages such as simple installation and maintenance, reduced weight and power requirement, easy sharing and control of global resource, as well as high flexibility and reliability. Therefore, during the past Manuscript received June 8, 2013; revised August 28, 2013; accepted October 1, 2013. Date of publication November 6, 2013; date of current version March 21, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 61203230, Grant 61273104, Grant 61333003, Grant 61210012, and Grant 61290324, in part by the National 973 Project under Grant 2010CB731800, in part by the China Postdoctoral Science Foundation under Grant 2013M530629, and in part by the Open Project of Key Laboratory of Wireless Sensor Network and Communication, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, China, under Grant 2012005. Z.-H. Pang is with the Key Laboratory of Fieldbus Technology and Automation of Beijing, North China University of Technology, Beijing 100144, China, and also with the Department of Automation, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). G.-P. Liu is with the School of Engineering, University of South Wales, Pontypridd, CF37 1DL, U.K., and also with the Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China. D. Zhou and M. Chen are with the Department of Automation, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2289890

decade, NCSs have been widely used in various industrial areas such as process control [1], intelligent transportation [2], robot control [3], wireless sensor networks [4], networked surgery [5], power systems [6], unmanned aerial vehicles [7], and webbased control laboratory [8]. However, the introduction of communication networks into control systems inevitably brings some adverse effects to NCSs, such as limited bandwidth, network-induced delay, packet disorder and dropout, quantization error, variable sampling interval, and clock synchronization [9]. These communication constraints can deteriorate the performance of NCSs or even make them unstable. Therefore, growing attention has been paid to the research of NCSs in the past decade, mainly on the issues of stability analysis and stabilization, state estimation, and network scheduling (see [10]–[12] and references therein). However, the problem of output tracking for NCSs has received relatively less attention because it is generally more challenging than the stabilization problem [13]. In recent years, only a few works have been concerned with the output tracking problem of NCSs [14]–[23]. A delaydependent tracking controller was designed for NCSs with Markov delays in [14] and [15]. However, only the networkinduced delay was considered, and the Markov transition matrices must be known in advance. The problem of H∞ model reference control for NCSs with network-induced delay and packet dropout was studied in [16]–[18], where a state feedback controller with the fixed gain was designed to guarantee the H∞ output tracking performance. However, a finite steadystate tracking error would exist, and further, the system state is required to be online measurable, which may be not available in practice. The decentralized H∞ control problem for a class of compartmental networks was studied in [19], while none of network communication constraints was considered. In [20], the formation tracking control for multiple spacecraft with network-induced delay and bounded external disturbance was investigated. Taking into account network-induced delay and packet dropout, some results on the tracking control problems of networked Takagi-Sugeno (T-S) fuzzy systems have been reported in [21] and [22] and the references therein. It should be noted that most of the aforementioned results have just been demonstrated by numerical simulations, except for the experimental test via a simulated network in [13]. However, the pure simulation cannot fully represent the characteristics of practical plants and networks, as well as the practical components of NCSs. This motivates us to study an output tracking control method for NCSs from the viewpoint of practical applications.

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In this paper, the output tracking control problem of networked systems is investigated. Among the communication constraints, the network-induced delay, packet disorder, and packet dropout are taken into consideration and, further in a unified way, are treated as the round-trip time (RTT) delay with an upper bound. By using the augmentation method, the output tracking problem of the NCS is transformed into the stabilization problem of an augmented system for all admissible RTT delays. Based on the estimated state increment and output tracking error, a model-based networked predictive output tracking control (NPOTC) scheme is proposed to compensate for the RTT delay, which avoids the requirement for the synchronization between the remote controller and the plant. Then, a two-stage delay-independent design strategy is presented for the NPOTC system, which can guarantee the closed-loop stability and also achieve the same output tracking performance as that of the corresponding LCS. The remainder of this paper is organized as follows. The problem of networked output tracking control (NOTC) is formulated in Section II. Section III presents a model-based NPOTC approach. The main results on stability analysis, controller design, and performance analysis are given in Section IV. Numerical simulations and practical experiments are conducted to show the performance of the proposed approach in Sections V and VI, respectively. Section VII concludes this paper. Notation: The notations used throughout this paper are fairly standard. R, Rn , and Rn×m denote the set of real numbers, the n-dimensional Euclidean space, and the set of n × m real matrices, respectively. The superscript “T” stands for matrix transposition. In and 0n×m denote the n-dimensional identity matrix and n × m zero matrix, respectively. The notation diag{· · ·} represents a block-diagonal matrix. Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations. II. P ROBLEM F ORMULATION

x(k + 1) = Ax(k) + Bu(k) y(k) = Cx(k)

(1)

where x(k) ∈ R , u(k) ∈ R , and y(k) ∈ R are the state, input, and output, respectively. A, B, and C are matrices with appropriate dimensions. Our purpose is to design a controller such that the output y(k) tracks a reference signal r(k). The tracking error is m

q

e(k) = r(k) − y(k).

(2)

System (1) can be written into an incremental form Δx(k + 1) = AΔx(k) + BΔu(k) Δy(k) = CΔx(k) where

⎧ ⎨ Δx(k) = x(k) − x(k − 1) Δu(k) = u(k) − u(k − 1) ⎩ Δy(k) = y(k) − y(k − 1).

NPOTC systems.

It learns from (2) and (3) that e(k+1) = e(k)−CAΔx(k)−CBΔu(k)+Δr(k+1)

(4)

where Δr(k + 1) = r(k + 1) − r(k) ∈ R . Then, from (3) and (4), we obtain the following augmented system: q

xe (k + 1) = Ae xe (k) + Be Δu(k) + Ee Δr(k + 1) Δy(k) = Ce xe (k) where

(5)

Δx(k) A 0n×q ∈ Rn¯ , Ae = , e(k) −CA Iq B 0 Be = , Ee = n×q , Ce = [ C 0q×q ] , −CB Iq

xe (k) =

n ¯ = n + q. Thus, the output tracking control problem of system (1) is converted into the stabilization problem of augmented system (5). In practical NCSs, there generally exist such communication constraints as network-induced delay, packet disorder, and packet dropout in the networks between the controller and the plant. In this paper, our task is to design a networked controller for system (5) such that the resulting closed-loop NCS is asymptotically stable. III. M ODEL -BASED NPOTC S CHEME

Consider the following discrete-time linear system:

n

Fig. 1.

(3)

The NPOTC scheme is shown in Fig. 1. It includes three parts: a data preprocessor (DP) and a network delay compensator (NDC) at the plant side and a control prediction generator (CPG) at the controller side. The DP is used to calculate the state increment estimation, output tracking error, and reference increment vector. The CPG is employed to generate a sequence of control increment predictions based on system model (5). The NDC is designed to select a proper control signal for the plant according to the RTT delay. The following assumptions are necessary for the design of the NPOTC system. Assumption 1: The sensor and actuator are time driven and synchronous, while the controller is event driven. Assumption 2: The random RTT delay τk has an upper bound τ¯, i.e., τk ≤ τ¯. Assumption 3: (A, B) is controllable, (A, C) is observable, A − In B and the matrix has a full row rank. C 0q×m Assumption 4: The packet transmitted through networks is with a time stamp.

PANG et al.: OUTPUT TRACKING CONTROL FOR NETWORKED SYSTEMS: A MODEL-BASED PREDICTION APPROACH

Remark 1: It is easy for smart sensors and actuators to perform some simple calculation locally [10]. Hence, the state increment estimation Δˆ x(k|k − 1) is calculated in the sensor, as shown in Fig. 1. Moreover, the output tracking error e(k) and the reference increment vector ΔR(k + 1) are generated in the sensor rather than in the controller, which avoids the synchronization between the sensor and controller. Remark 2: The disordered packet in the actuator is discarded and essentially amounts to a packet dropout. However, the disordered packet in the controller is not rejected since the control packet that is generated from this disordered feedback packet may not keep disordered when arriving at the actuator. In order to describe the network-induced delay, packet disorder, and packet dropout in a unified way, the RTT delay τk is redefined in this paper, which denotes the total time delay of the packet successfully arriving at the actuator in order. The RTT delay can be obtained in the actuator by subtracting the time stamp of the latest control packet from the current time of the actuator at each sampling instant. As a result, it naturally includes the network-induced delay, packet disorder, and packet dropout in both communication channels. A. Design of DP To obtain the state increment estimation Δˆ x(k|k − 1) in the sensor, the following observer is designed: Δˆ x(k + 1|k) = AΔˆ x(k|k − 1) + BΔu(k) +L (Δy(k) − CΔˆ x(k|k − 1)) .

(6)

At each sampling instant, the sensor sends the following feedback packet together with the time stamp to the controller: T ê (ks |ks − 1)T ΔR(ks + 1)T (7) Dks = x T

where x ê (ks |ks − 1) = [Δˆ x(ks |ks − 1)T e(ks )T ] , ΔR(ks + T 1) = [Δr(ks + 1) Δr(ks + 2)T · · · Δr(ks + τ¯)T ]T , and ks is a time stamp. ΔR(ks + 1) is assumed to be available at time ks .

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for i = 1, 2, . . . , τ¯. Clearly, (8) and (10) yield the following control increment prediction sequence: T u(ks |ks )T Δˆ u(ks + 1|ks )T · · · Δˆ u(ks + τ¯|ks )T . ΔUks = Δˆ (11) Then, the sum of control increments is obtained as follows: Δˆ us (ks + i|ks ) =

i

Δˆ u(ks + j|ks )

for i = 0, 1, 2, . . . , τ¯, which produces the following control prediction sequence: T ΔUkss = Δˆ us (ks |ks )TΔˆ us (ks +1|ks )T · · ·Δˆ us (ks + τ¯|ks )T . (13) It is packed together with the time stamp ks and transmitted to the actuator. C. Design of NDC Due to the random delay, packet disorder, and packet dropout in the forward channel, it probably happens that zero, one, or more control packets arrive at the actuator during one sampling interval. The NDC is designed to preserve the latest control prediction sequence ΔUkss∗ and the corresponding time stamp ks∗ available in the actuator. That is, it performs the following updating process at each sampling instant:

ΔU s , if ks > k ∗ s ΔUks∗ = ΔUkss , if k ≤ ks∗ or no packets arrive (14) s s ks∗

ks , if ks > ks∗ (15) ks∗ = ks∗ , if ks ≤ ks∗ or no packets arrive where ΔUkss∗ can be described by T ΔUkss∗ = Δˆ us (ks∗|ks∗ )T Δˆ us (ks∗+1|ks∗ )T · · ·Δˆ us (ks∗+ τ¯|ks∗ )T . (16) At each execution instant k, the real-time RTT delay can be calculated in the actuator as follows: τk = k − ks∗

B. Design of CPG The CPG is designed based on the following state feedback control strategy: ê (ks |ks − 1) Δˆ u(ks |ks ) = −K x

(8)

where K ∈ Rm×n is the gain matrix to be determined. By the iteration of (5) and (8), the predictions of the augmented state and control increment up to time ks + τ¯ are obtained as follows: ê (ks + i − 1|ks − 1) x ê (ks + i|ks − 1) = Ae x +Be Δˆ u(ks +i−1|ks )+Ee Δr(ks +i) (9) Δˆ u(ks + i|ks ) = − K x ê (ks + i|ks − 1)

(10)

(12)

j=0

(17)

where τk ≤ τ¯ is a nonnegative integer. In order to compensate for the RTT delay τk , the NDC applies the following control signal to the plant at time k: u(k) = u (ks∗ − 1) + ΔUkss∗ (τk ) = u (ks∗ − 1) + Δˆ us (ks∗ + τk |ks∗ ) = u(k − τk − 1) + Δˆ us (k|k − τk ).

(18)

Remark 3: According to the aforementioned delay compensation strategy, a proper control signal is selected for the plant according to the RTT delay. However, due to the networks between the controller and actuator, the controller cannot know which control signal is selected. As a result, the control input u(ks − 1) cannot be found exactly in the controller. On the contrary, u(ks − 1) is always available in the actuator at time k when a buffer is built for historical control inputs. Therefore,

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the calculation of the control signal is carried out in the actuator rather than in the controller, as shown in (18). Remark 4: In general, the event-driven mode has some advantages for NCSs such as clock-free and better resource utilization. Therefore, the event-driven controller and actuator were widely used, for instance, in [16], [17], and [20]. However, the time-driven actuator is adopted in this paper. With the help of the proposed delay compensation strategy, the random RTT delay can still be compensated even if no control packets arrive at the actuator during a certain control cycle. Thus, the actuator needs to be time driven and performed periodically.

A. Closed-Loop Stability Analysis To analyze the stability, let the reference input r(·) = 0. From the aforementioned NPOTC strategy, the utilized control increment for augmented system (5) at time k is (19)

which can be learned from (10), (17), and (18). The state increment observer (6) can be rewritten as Δˆ x(k + 1|k) = AΔˆ x(k|k − 1) + BΔu(k) + LC x ˜(k) (20) where x ˜(k) = Δx(k) − Δˆ x(k|k − 1). Subtracting (20) from (3) results in the following equation: x ˜(k + 1) = (A − LC)˜ x(k).

(21)

Equation (4) can be rewritten as e(k + 1) = e(k) − CA (Δˆ x(k|k − 1) + x ˜(k)) − CBΔu(k). (22) From (20) and (22), we obtain ê (k|k − 1) + Be Δu(k) + A1 x ˜(k) (23) x ê (k + 1|k) = Ae x where

x ê (k|k − 1) =

Δˆ x(k|k − 1) ∈ Rn¯ , e(k)

A1 =

LC . −CA

Using (17), (9) can be rewritten as ê (k|k − τk − 1) + Be Δu(k). x ê (k + 1|k − τk − 1) = Ae x (24) Subtracting (24) from (23) leads to ˜e (k) + A1 x ˜(k) x ˜e (k + 1) = Ae x

(25)

where x ˜e (k − i) = x ê (k − i|k − i − 1) − x ê (k − i|k − τk − 1) for the integer i ≤ τk . From (25), we have x ˜e (k) = Aτek x ˜e (k − τk ) +

τk

=

i=1

Ai−1 ˜(k − i). e A1 x

= (Ae − Be K)xe (k) + Be K (xe (k) − x ê (k|k − 1) + x ˜e (k)) = (Ae − Be K)xe (k)

τk i−1 ˜(k) + Ae A1 x ˜(k − i) (27) + Be K I¯x i=1

X(k + 1) = Λτk X(k)

(28)

where X(k) ∈ Rn¯ +(¯τ +1)n , Θτk ∈ Rn¯ ×(¯τ +1)n , and ⎡ ⎤ xe (k) ˜(k) ⎥ ⎢ x Ae − Be K Θτk ⎢ ⎥ X(k) = ⎢ x ˜(k − 1) ⎥ , Λτk = 0 Γ ⎣ ⎦ ··· x ˜(k − τ¯) Θτk = Be K I¯ A1 Ae A1 A2e A1 · · · Aτek A1 0n¯ ×(¯τ −τk )n Γ = diag{A − LC A − LC · · · A − LC} ∈ R(¯τ +1)n×(¯τ +1)n . Theorem 1: The closed-loop system (28) is globally uniformly asymptotically stable (GUAS) if and only if the eigenvalues of matrices (Ae − Be K) and (A − LC) are within the unit circle. Proof: Since the RTT delay τk randomly takes values in the finite set {0, 1, 2, . . . , τ¯}, system (28) is a linear switched system. It is well known that a block upper triangular linear switched system is GUAS under arbitrary switching if and only if each block-diagonal subsystem is GUAS under arbitrary switching (see [24] and [25]). The proof is completed. Remark 5: The stability condition of the closed-loop NCS resulting from augmented system (5) is given in Theorem 1. For the output tracking problem, what is mainly concerned with is the output tracking performance. It can be seen from Theorem 1 that, if the closed-loop system (28) is GUAS, xe (k) tends to zero with respect to time, i.e., e(k) → 0 and Δx(k) → 0 as k → ∞. At the same time, the closed-loop stability of the original system (1) can be also guaranteed, of which the detailed explanation is given in the Appendix. Remark 6: It is clear from Theorem 1 that the stability of the closed-loop NPOTC system is independent of the RTT delay, which would simplify the design of NPOTC systems. B. Output Tracking Controller Design

Ai−1 ˜(k − i) e A1 x

i=1 τk

xe (k + 1) = Ae xe (k) + Be Δu(k)

where I¯ = [In 0n×q ]T . The combination of (21) and (27) leads to the following closed-loop system:

IV. A NALYSIS OF S TABILITY AND P ERFORMANCE

Δu(k) = Δˆ u (ks∗ + τk |ks∗ ) = −K x ê (k|k − τk − 1)

Then, it can be obtained from (5), (19), and (26) that

(26)

It can be seen from the aforementioned stability analysis that the separation principle for the design of the observer-based controller is still held in the NPOTC system. Therefore, the following two-stage controller design scheme is presented.


1) Design of State Increment Observer: The design of the observer gain matrix L in (6) can follow the design procedure of LCS (3). 2) Design of State Feedback Controller: The design of the controller gain matrix K in (8) can follow the design procedure of LCS (5).

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TABLE I RUNNING P ROCESS OF NPOTC S YSTEM

C. Output Tracking Performance Analysis Theorem 2: For time-varying reference signals r(k) = y0 for k < τ¯, where y0 is a steady-state value of the output y(k), the NPOTC system can achieve the same output tracking performance as that of the corresponding LCS. Proof: To begin with, consider a single-input singleoutput (SISO) system with the steady-state values y(k) = y0 and u(k − 1) = u0 for k ≤ 0, where y0 and u0 are constant real numbers. The initial state increment of observer (6) is set to be Δˆ x(0| − 1) = 0. With Δx(0) = 0, it can be obtained from (21) that Δˆ x(k|k − 1) = Δx(k) for all k ≥ 0. That is, x ê (k|k − 1) = xe (k)

(29)

for all k ≥ 0. For the reference signals r(k) = y0 for k < τ¯, from (7), we have ΔR(2) = [0 0 · · · 0 Δr(¯ τ ) Δr(¯ τ + 1)]T (30)

According to the delay compensation strategy in (19), it can be deduced that, at each instant k = 0, 1, 2, . . . , τ¯ − 1, whether the actuator receives any control packets, the control increment applied to system (5) is always Δu(k) = 0. Thus, it is clear from (3) and (6) that Δˆ x(k|k − 1) = Δx(k) = 0 for k = 1, 2, · · · , τ¯, and thus, the following feedback packets are sent to the controller: T (31) Dk = 01×¯n ΔR(k + 1)T T Dτ¯ = xe (¯ τ )T ΔR(¯ τ + 1)T (32) τ ) = [01×n Δr(¯ τ )]T = for k = 0, 1, 2, . . . , τ¯ − 1, where xe (¯ Ee Δr(¯ τ ). Using (8)–(10), the following control increment prediction sequences can be calculated in the CPG: T (33) ΔUk = − 01×(¯τ −k) KF0 KF1 KF2 · · · KFk for k = 0, 1, 2, . . . , τ¯, where Fk =

by the NDC at time k = τ¯. Using (17), (19), and (33), τ5 = 5 − 2 = 3, and Δu(5) = ΔU2 (τ5 ) = −KF0 . Then, from (5), (7), and (11), it can be obtained that τ +1) = (Ae −Be K)Ee Δr(¯ τ )+Ee Δr(¯ τ +1) = F1 xe (¯ T τ +1)T ΔR(¯ τ +2)T Dτ¯+1 = xe (¯ ΔUτ¯+1 = − [KF1 KF2 · · · KFτ¯+1 ]T .

ΔR(1) = [0 0 · · · 0 0 Δr(¯ τ )]T ΔR(3) = [0 0 · · · Δr(¯ τ ) Δr(¯ τ + 1) Δr(¯ τ + 2)]T ···.

TABLE II RUNNING P ROCESS OF LOTC S YSTEM

k (Ae − Be K)k−i Ee Δr(¯ τ + i). i=0

At time k = τ¯, due to the upper bound τ¯ of the RTT delay, at least one of the control increment packets in (33) is available in the actuator. No matter which packet is selected by the NDC, the control increment applied to system (5) must be Δu(¯ τ ) = −KF0 according to the compensation strategy of NDC. For example, suppose that τ¯ = 5 and ΔU2 is selected

(34) (35) (36)

Similarly, it can be obtained that the utilized control increment is Δu(¯ τ + 1) = −KF1 at time k = τ¯ + 1. As a result, it can be deduced that xe (k) = Fk−¯τ T Dk = xe (k)T ΔR(k + 1)T ΔUk = − [KFk−¯τ KFk−¯τ +1 · · · KFk ]T Δu(k) = − KFk−¯τ

(37) (38) (39) (40)

for all k ≥ τ¯. The running process of the NPOTC system is given in detail in Table I. With the reference signals r(k) = y0 for k < τ¯ and with Δˆ x(0| − 1) = Δx(0) = 0, the control law in (8) is employed for the local control of system (5), which produces the augmented state and control increment shown in Table II. It can be concluded from the comparison between Tables I and II that the NPOTC system achieves the same output tracking performance as that of the corresponding LCS. For multiple-input multiple-output (MIMO) systems, the similar results like Tables I and II can be obtained using the same procedure, except that the dimensions of xe (k), Dk , ΔUk , and Δu(k) are different. The proof is completed. Theorem 3: For the step reference signal, the NPOTC system can achieve a zero steady-state output tracking error if the closed-loop system is GUAS. Proof: We first consider the case of SISO systems. With the following step reference signal:

k < τ¯ y0 , (41) r(k) = y0 + r¯, k ≥ τ¯

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where r¯ ∈ R is a constant, it is obtained from (37) that xe (k) =

k−¯ τ

(Ae − Be K)k−¯τ −i Ee Δr(¯ τ + i)

i=0

= (Ae − Be K)k−¯τ Ee r¯

(42)

for k ≥ τ¯. Since the eigenvalues of matrix (Ae − Be K) are within the unit circle, we have xe (k) → 0 (i.e., Δx(k) → 0 and e(k) → 0) with k → ∞. Therefore, the NPOTC method can achieve a zero steady-state output tracking error for the step reference signal. Using the similar procedure, the same conclusion can be also reached for MIMO systems. The proof is completed. Remark 7: The proposed NPOTC scheme belongs to the networked predictive control (NPC) methodology, which can be traced back to [26]. Compared with previous NPC methods in [13], [14], and [27]–[32], the NPOTC scheme has the following advantages: 1) The packet dropout is treated as a part of the RTT delay, which was also used in [29] and [33], and this avoids the transmission of additional candidate data that was adopted in [27] and [28] to deal with the effect of consecutive packet dropouts; 2) the NPOTC method is easy to be implemented in practice since it removes the requirement for the synchronization between the controller and the plant, and also, the generation of control increment predictions is only based on the delayed data in (7); 3) the closed-loop stability of the NPOTC system is not related to the network-induced delay, packet disorder, and packet dropout, and the similar conclusion was also obtained in [28]; however, the NPC method in [28] needs the synchronization between network nodes, and also, a steady-state error would exist in the resulting NPC system; and 4) the NPOTC system can achieve the same output tracking performance as that of the corresponding LCS. V. S IMULATION R ESULTS To illustrate the NPOTC approach, a servo motor system (SMS) is considered, whose input and output are the control voltage (in volts) and the angle position (in degrees), respectively. For the sampling period of 0.04 s, the state-space model is identified to be x(k + 1) = Ax(k) + Bu(k) y(k) = Cx(k) where

⎡

A=⎣

1.2998 1 0

C = [ c1

c2

−0.4341 0 1

(43) ⎤

⎡ ⎤ 1 B = ⎣0⎦ 0

2.7739

1.0121 ] .

0.1343 0 ⎦, 0

c3 ] = [ 3.5629

The initial values of the system state and the observer state are set to be [−8.1645 − 8.1645 − 8.1645]T (which corresponds to y(0) = −60) and [0 0 0]T , respectively. The desired poles of the observer (6) and the closed-loop system (5) are chosen as [0.5 0.3 0.1] and [0.6 ± 0.3j 0.2 0.1], respectively.

Fig. 2.

LOTC (simulation case).

By using the pole assignment method, the observer gain matrix L and the controller gain matrix K are designed to be 0.1470]T

L = [0.0363

0.0439

K = [0.7125

− 0.2593

0.1253

(44) − 0.0245].

(45)

In the following numerical simulations, the reference signal r(k) is chosen as a square wave between −60 and 60 with the period of 10 s, and three cases are considered for simulations. A. LOTC The simulation result of the local output tracking control (LOTC) system is shown in Fig. 2, which indicates that the output tracking performance is well achieved. B. NOTC The sensor and actuator are set to be time driven and synchronous, and the controller is event driven. With 1- and 3-step constant RTT delays, respectively, the performance of the NOTC system without network delay compensation is shown in Fig. 3(a). The simulation results confirm that, as the RTT delay increases, the output tracking performance rapidly degrades. When the RTT delay is randomly chosen to be 3–8 steps, as shown in Fig. 3(b), the simulation result is shown in Fig. 3(c), from which we can see that the closed-loop NOTC system becomes unstable. C. NPOTC 1) NPOTC Without Disturbance and Model Mismatch: With the random RTT delay of 3–8 steps shown in Fig. 4(a), the simulation result of the NPOTC system is given in Fig. 4(b), which indicates that the closed-loop system is still stable. Furthermore, the performance of the NPOTC system (solid line) is the same as that of the LOTC system (dotted line), which coincides with the results of the output tracking performance analysis in Section IV-C. 2) NPOTC With Measurement Noise: The design and analysis of the NPOTC system in this paper is based on the nominal model (1), but no practical systems are without disturbance. To show the capability of the NPOTC method in handling


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Fig. 4. NPOTC (simulation case). (a) Random RTT delays (3–8 steps). (b) Tracking performance.

Fig. 3. NOTC (simulation case). (a) Tracking performance under constant RTT delays. (b) Random RTT delays (3–8 steps). (c) Tracking performance under random RTT delays (3–8 steps).

disturbance, the uniform random noise distributed in [−2, 2] shown in Fig. 5(a) is added to the output y(k). With the random RTT delay of 3–8 steps shown in Fig. 4(a), the simulation result of the NPOTC system is shown in Fig. 5(b). It can be seen that the NPOTC system still keeps stable and also provides a good tracking performance. 3) NPOTC With Model Mismatch: To illustrate the performance of the NPOTC system with model mismatch, the matrices A and B in (43) and the following matrix Cmm are used to design the CPG for the control of system (43): Cmm = [0.8c1

0.7c2

0.6c3 ] = [2.8503

1.9417

0.6073]. (46)

For the same closed-loop poles [0.6 ± 0.3j 0.2 0.1], the control gain matrix Kmm = [0.7048 − 0.2639 0.1253 − 0.0333] is

Fig. 5. NPOTC with measurement noise (simulation case). (a) Uniform random measurement noise. (b) Tracking performance.

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TABLE III S TATISTICS OF RTT D ELAYS

Fig. 6. NPOTC with model mismatch (simulation case).

Fig. 8.

Fig. 7. Internet-based SMS.

obtained. The simulation result of the NPOTC system is shown in Fig. 6. It can be seen that, with the model mismatch in (46) and the random RTT delay of 3–8 steps shown in Fig. 4(a), the closed-loop NPOTC system is stable, and the output tracking error ultimately converges to zero. However, due to the model mismatch in (46), the error between the predicted state in (9) and the real state is generated, which results in the degradation of the tracking performance of the NPOTC system. VI. E XPERIMENTAL R ESULTS A. Internet-Based SMS To validate the proposed NPOTC method on practical systems, an Internet-based SMS test rig has been constructed, as shown in Fig. 7. It is made up of a networked controller board (NCB), a networked implementation board (NIB), an SMS, as well as the Internet. The SMS is located in the University of South Wales, Pontypridd, U.K., and used as the plant for the position control. The NIB (193.63.131.219) is directly connected with the SMS via wires, which is used as the interface between the SMS and the Internet. The NCB (166.111.72.24) is placed in Tsinghua University, Beijing, China, which is linked with the NIB through the Internet and utilized for the implementation of networked control strategies. The NCB and NIB have the same hardware structure [33]. The former is set to be event driven, and the latter is time driven. The SMS is composed of a dc motor, a load plate, and an angle

RTT delays between the NCB (China) and NIB (U.K.).

sensor. The dc motor is driven by a servo amplifier of which the input ranges from −10 to 10 V. The angle sensor is used to measure the angle position of the dc motor with the output ranging from −10 to 10 V, which corresponds to the angle of the load plate from −120◦ to 120◦ . Before performing control experiments, we need to know the characteristics of the Internet between the NCB and NIB. The sampling period is set to be 0.04 s in the NIB. According to the practical experiments of 24 h, the RTT delays are obtained and vary from 3 to 8 steps (0.12–0.32 s), which are shown in Table III. Fig. 8 gives a real-time record of RTT delays in an hour from 15:00:00 to 16:00:00 (Beijing time) on May 17, 2013. It can be seen that the RTT delays are bounded with 4 and 7 and may keep constant in a certain period of time, for instance, 4 steps from k = 1409.12 s to k = 1704.08 s. B. Practical Experiments The SMS in Fig. 7 is nonlinear with disturbance in nature. A simplified linear model shown in (43) is identified for the SMS, which is used to design the observer (6) and the controller (8). Therefore, the gain matrices L and K in the following experiments are chosen to be the same as those in the simulations shown in (44) and (45). The reference signal r(k) is chosen as a sine wave with the amplitude of 60◦ and the period of 10 s. The practical experiments on the SMS are also carried out for three cases. 1) LOTC: Only the NIB is used for the local control of the SMS. The experimental result is shown in Fig. 9, which indicates that the output of the SMS tracks well the sinusoidal reference signal. 2) NOTC: With the RTT delay of 3–8 steps in Table III and Fig. 8, the performance of the NOTC system without network delay compensation is shown in Fig. 10. It is clear that the RTT delay leads to the instability of the NOTC system.


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VII. C ONCLUSION This paper has investigated the problem of output tracking for NCSs. The problem is solved by using a model-based prediction approach, which has taken the network-induced delay, packet disorder, and packet dropout into consideration. A two-stage controller design procedure has been presented, which guarantees simultaneously the closed-loop stability and the desired output tracking performance. From theoretical analysis, simulation results, and experimental results, we can draw the following conclusions.

Fig. 9.

LOTC (experimental case).

Fig. 10. NOTC (experimental case).

1) The RTT delay redefined in this paper can describe the total effects of the network-induced delay, packet disorder, and packet dropout. Based on the RTT delay, a modelbased NPOTC method via augmented state feedback control has been proposed, which is easy to be implemented in practice. 2) The stability of the closed-loop NPOTC system has been proved to be not related to the RTT delay, which is also confirmed via numerical simulations and practical experiments. Furthermore, the separation principle for the design of the observer-based controller is also held in the NPOTC system. 3) Both the performance analysis and simulation results have shown that, for time-varying reference signals, the NPOTC system can achieve the same output tracking performance as that of the LOTC system. Moreover, the capability of the NPOTC method in handling measurement noise and model mismatch has been tested via simulations. It is worth mentioning that, due to the difference between the utilized linear model and the practical plant, the NPOTC system gives a little worse performance than that of the LOTC system.

A PPENDIX F URTHER E XPLANATION OF R EMARK 5

Fig. 11. NPOTC (experimental case).

3) NPOTC: The linear model (43) is used for the design of CPG. With the RTT delay of 3–8 steps in Table III and Fig. 8, the experimental result of the NPOTC system is shown in Fig. 11, which indicates that the output tracking performance is good. It should be noted that, by comparing Fig. 11 with Fig. 9, the performance of the NPOTC system is slightly inferior to that of the LOTC system. The reason is that the practical issues such as the static friction, dead zone, and hardware constraints are inevitable in the experiments, and thus, the utilized model (43) cannot fully describe the practical SMS.

When the closed-loop system (28) is GUAS, it can be obtained that Δx(k) → 0, e(k) → 0, and x ˜(k) → 0 as k → ∞. From Assumption 3, we know that m ≥ q. Therefore, the following two cases are considered for the closed-loop stability of the original system (1). 1) If m > q: With Δx(∞) = 0, y(∞) = 0, and x ˜(∞) = 0, it can be deduced from (1) and (8) that the state x(k) and input u(k) are bounded. Therefore, the output of the closedloop system of (1) is GUAS with the bounded state and input. 2) If m = q: It learns from (1) that

A − In C

B 0q×m

x(∞) = 0n¯ ×1 . u(∞)

(47)

A − In B From Assumption 3, we know that is invertC 0q×m ible. Then, it can be obtained that the original state x(∞) converges to zero. Therefore, the closed-loop NCS of the original system (1) is GUAS.

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Zhong-Hua Pang (M’11) received the B.Eng. degree in automation and the M.Eng. degree in control theory and control engineering from Qingdao University of Science and Technology, Qingdao, China, in 2002 and 2005, respectively, and the Ph.D. degree in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences, Beijing, China, in 2011. He is currently a Postdoctoral Researcher with the Department of Automation, Tsinghua University, Beijing, and an Associate Professor with the School of Mechanical and Electrical Engineering, North China University of Technology, Beijing. His research interests include networked control systems and advanced control of industrial systems.

Guo-Ping Liu (F’11) received the B.Eng. and M.Eng. degrees in automation from Central South University of Technology (now Central South University), Changsha, China, in 1982 and 1985, respectively, and the Ph.D. degree in control engineering from the University of Manchester Institute of Science and Technology (now University of Manchester), Manchester, U.K., in 1992. He is Chair of Control Engineering at the University of South Wales, Pontypridd, U.K. He has been a Professor at the University of South Wales (formerly the University of Glamorgan) since 2004, a Hundred-Talent Program Visiting Professor at the Chinese Academy of Sciences, Beijing, China, since 2001, and a Changjiang Scholar Visiting Professor at Harbin Institute of Technology, Harbin, China, since 2008. He is the Editor-in-Chief of the International Journal of Automation and Computing. He has more than 400 publications on control systems and has authored/coauthored eight books. His main research areas include networked control systems, nonlinear system identification and control, advanced control of industrial systems, and multiobjective optimization and control.


Donghua Zhou (SM’99) received the B.Eng., M.Sci., and Ph.D. degrees from Shanghai Jiaotong University, Shanghai, China, in 1985, 1988, and 1990, respectively. He was an Alexander von Humboldt Research Fellow (1995–1996) at the University of Duisburg, Essen, Germany, and a Visiting Scholar at Yale University, New Haven, CT, USA (July 2001–January 2002). He is currently a Professor and the Head of the Department of Automation, Tsinghua University, Beijing, China. He has published over 110 peerreviewed international journal papers and four monographs in the areas of fault diagnosis and fault-tolerant control, reliability prediction, and predictive maintenance. Dr. Zhou is a member of the International Federation of Automatic Control (IFAC) Technical Committee on Fault Diagnosis and Safety of Technical Processes, an Associate Editor of the Journal of Process Control, the Deputy General Secretary of the Chinese Association of Automation (CAA), and a council member of CAA. He was also the National Organizing Committee Chair of the 6th IFAC Symposium on SAFEPROCESS in 2006.

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Maoyin Chen received the B.S. degree in mathematics and the M.S. degree in control theory and control engineering from Qufu Normal University, Rizhao, China, in 1997 and 2000, respectively, and the Ph.D. degree in control theory and control engineering from Shanghai Jiaotong University, Shanghai, China, in 2003. From 2003 to 2005, he was a Postdoctoral Researcher in the Department of Automation, Tsinghua University, Beijing, China. From October 2005 to October 2008, he was an Assistant Researcher in the Department of Automation, Tsinghua University. Since October 2008, he has been an Associate Professor in the Department of Automation, Tsinghua University. His research interests are in the areas of reliability analysis, fault prognosis, and predictive maintenance.