**4.4 General process of co-design methods**

The general process of the co-design methods is (see Fig. 2):


Fig. 2. General method of co-design of NCS scheduling and control

Predictive Control Applied to Networked Control Systems 79

( 1) ( ) ( ) ( 1)

*T As T*

( 1) ( ) ( )

*k 0*

*0*

*Γ*

0.2625 0.629 0.0561 ( 1) () () 0.0561 0.9618 0.0034

0.2625 0.629 0.0561 0 ( 1) 0.0561 0.9618 0.0034 ( ) 0 ( )

*k k k*

The simulation model structure of co-design of the networked control system with three loops is illustrated by Fig. 3. Controllers, actuators and sensors choose a Truetime kernel models respectively, the joint design optimization module in Fig.3 contains control parameter model and scheduling parameter model, and acts on the sensors and controllers

 1, 10, 0.1 ; network parameters: CAN bus network, transmission rate is 800kbps, scheduling algorithm is EDF, reference input signal is step signal, amplitude is 500. Loop1: initial sampling period 1 *T ms* 10 , size of data packet: 100bits, transmission time:

Loop2: initial sampling period 2 *T ms* 10 , size of data packet: 90bits, transmission time:

*z z u*

0 00 1

*yy y u u* ( ) 1.224 ( 1) 0.2878 ( 2) 0.5282 ( 2) 0.3503 ( 3) *kk k k k* (28)

*k k k*

*k kk*

*z Φ z Bu*

() ()

*0*

*0 0* ,

*0*

*B*

The initial sampling period 10 *T ms* , so the discretization model of DC servo motor is:

 *x x u*

*k k* 

*e ds <sup>1</sup> <sup>Γ</sup> <sup>B</sup>* .

*y Cx* (24)

*y Cz* (25)

*<sup>I</sup>* , [ 0] *C0 <sup>C</sup>*

*k k kx u z* , the above equation (24)

(26)

(27)

, quantization weights:

*k kkk*

 *d 01 x Ax Γ u Γ u*

To discretize equation (22), and suppose the delay of NCS is stochastic, then

() ()

*<sup>0</sup> <sup>Γ</sup> <sup>B</sup>* , *<sup>k</sup>*

Then introducing the augmented state vector 1 () [ ] *T TT*

 *d 1*

*A Γ*

( ) [0 155.35] ( )

( ) [0 155.35 0 ] ( )

Convert the state space model of augment system to the CARIMA form:

of three loops, in order to optimize system operating parameters in real time.

The initial value of GPC control parameters: 2 *M* , 20 *P* , 0.1

*k k*

*y z*

*k k*

*y x*

*k*

*Φ*

The corresponding augmented matrix is:

12 3

 

<sup>1</sup>*c m* 100 8 /800000 1 *s* ;

<sup>2</sup> *c ms* 0.9 ;

*<sup>T</sup> <sup>k</sup> As e ds* 

where, *AT <sup>e</sup> Ad* , <sup>0</sup>

can be rewritten as follows:

*k k*

To facilitate the research of co-design, the algorithm proposed in this chapter can be extended to co-design of the other control and scheduling algorithms. And we can replace GPC with the other control algorithms and replace EDF with the other scheduling algorithms. The design idea and process are similar to the co-design algorithm presented in this chapter.

### **5. Simulation experiments**

#### **5.1 Simulation models and parameters' settings**

In this chapter, NCS of three loops are used, the plants are the three DC (Direct Current) servo motors, and all the three loops have the same control architecture. The transfer function model of DC servo motor is:

$$G(s) = \frac{w(s)}{\mathcal{U}\_a(s)} = \frac{155.35}{s^2 + 12.46s + 11.2} \tag{20}$$

The transfer function is converted into a state-space expression:

$$\begin{cases} \dot{\mathbf{x}}(t) = A\mathbf{x}(t) + B\mathbf{u}(t) \\ \mathbf{y}(t) = \mathbf{C}\mathbf{x}(t) \end{cases} \tag{21}$$

$$\mathbf{A} = \begin{bmatrix} -12.46 & -11.2 \\ 0 & 1 \end{bmatrix}, \quad \mathbf{B} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}, \quad \mathbf{C} = \begin{bmatrix} 0 & 155.35 \end{bmatrix} \circ \mathbf{B}$$

We can suppose that:


At the sampling instant *th k* , when the controller is event driven, after the outputs of the plant reach the controller nodes, they can be immediately calculated by the control algorithm and sent control signals, similarly, actuator nodes execute control commands at the instant of control signals arrived.

Let *<sup>k</sup>* be the network induce delay, then

$$
\pi\_k = \pi\_{sc} + \pi\_{ca} \tag{22}
$$

where *sc* is the delay from sensor nodes to control nodes, *ca* is the delay from control nodes to actuator nodes.

Suppose *<sup>k</sup> T* , as the network induce delay exists in the system, the control input of the plant is piecewise constant values in a period, the control input which actuator received can be expressed by(23) (Zhang & Kong,2001):

$$\mathbf{w}(t) = \begin{cases} \mathfrak{u}(k-1), & t\_k < t \le t\_k + \tau\_k \\ \mathfrak{u}(k), & t\_k + \tau\_k < t \le t\_k + T \end{cases} \tag{23}$$

78 Frontiers of Model Predictive Control

To facilitate the research of co-design, the algorithm proposed in this chapter can be extended to co-design of the other control and scheduling algorithms. And we can replace GPC with the other control algorithms and replace EDF with the other scheduling algorithms. The design idea and process are similar to the co-design algorithm presented in

In this chapter, NCS of three loops are used, the plants are the three DC (Direct Current) servo motors, and all the three loops have the same control architecture. The transfer

> 2 ( ) 155.35 ( )

> > () () ()

*ttt*

1. Sensor nodes use the time-driven, the output of the plant is periodically sampled, and

At the sampling instant *th k* , when the controller is event driven, after the outputs of the plant reach the controller nodes, they can be immediately calculated by the control algorithm and sent control signals, similarly, actuator nodes execute control commands at

*k sc ca*

plant is piecewise constant values in a period, the control input which actuator received can

*k t tt*

*<sup>k</sup> T* , as the network induce delay exists in the system, the control input of the

*k kk kk k*

*k t tt T*

 

is the delay from sensor nodes to control nodes, *ca*

( 1), ( ) ( ),

*u*

*t*

*v*

() ()

*t t x Ax Bu*

*U s s s*

*w s G s*

The transfer function is converted into a state-space expression:

12.46 11.2 0 1 *<sup>A</sup>* , <sup>1</sup>

2. Controller nodes and actuator nodes use event-driven.

*<sup>a</sup>*( ) 12.46 11.2

0  (20)

*y Cx* (21)

(22)

is the delay from control

*<sup>u</sup>* (23)

*B* , *C* 0 155.35 。

this chapter.

**5. Simulation experiments** 

We can suppose that:

Let *<sup>k</sup>* 

where *sc* 

Suppose

nodes to actuator nodes.

sampling period is *T* .

the instant of control signals arrived.

be the network induce delay, then

be expressed by(23) (Zhang & Kong,2001):

function model of DC servo motor is:

**5.1 Simulation models and parameters' settings** 

To discretize equation (22), and suppose the delay of NCS is stochastic, then

$$\begin{cases} \mathbf{x}(k+1) = A\_d \mathbf{x}(k) + \Gamma\_\theta \mathbf{u}(k) + \Gamma\_I \mathbf{u}(k-1) \\ \mathbf{y}(k) = \mathbf{C} \mathbf{x}(k) \end{cases} \tag{24}$$

where, *AT <sup>e</sup> Ad* , <sup>0</sup> *<sup>T</sup> <sup>k</sup> As e ds <sup>0</sup> <sup>Γ</sup> <sup>B</sup>* , *<sup>k</sup> T As T e ds <sup>1</sup> <sup>Γ</sup> <sup>B</sup>* .

*Φ*

Then introducing the augmented state vector 1 () [ ] *T TT k k kx u z* , the above equation (24) can be rewritten as follows:

$$\begin{cases} z(k+1) = \Phi\_k z(k) + \mathcal{B}\_\theta \mu(k) \\ y(k) = \mathcal{C}\_\theta z(k) \end{cases} \tag{25}$$
 
$$\mathcal{C}\_k = \begin{bmatrix} A\_d & \Gamma\_I \\ \mathbf{0} & \mathbf{0} \end{bmatrix}, \quad \mathcal{B}\_\theta = \begin{bmatrix} \Gamma\_\theta \\ & I \end{bmatrix}, \quad \mathcal{C}\_\theta = \begin{bmatrix} \mathbf{C} & \mathbf{0} \end{bmatrix}$$

The initial sampling period 10 *T ms* , so the discretization model of DC servo motor is:

$$\begin{cases} \mathbf{x}(k+1) = \begin{bmatrix} 0.2625 & -0.629 \\ 0.0561 & 0.9618 \end{bmatrix} \mathbf{x}(k) + \begin{bmatrix} 0.0561 \\ 0.0034 \end{bmatrix} \mathbf{u}(k) \\ \mathbf{y}(k) = \begin{bmatrix} 0 & 155.35 \end{bmatrix} \mathbf{x}(k) \end{cases} \tag{26}$$

The corresponding augmented matrix is:

$$\begin{cases} \mathbf{z}(k+1) = \begin{bmatrix} 0.2625 & -0.629 & 0.0561 \\ 0.0561 & 0.9618 & 0.0034 \\ 0 & 0 & 0 \end{bmatrix} \mathbf{z}(k) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \mathbf{u}(k) \\ \mathbf{y}(k) = \begin{bmatrix} 0 & 155.35 & 0 \end{bmatrix} \mathbf{z}(k) \end{cases} \tag{27}$$

Convert the state space model of augment system to the CARIMA form:

$$\mathbf{y}(k) = 1.224\mathbf{y}(k-1) - 0.2878\mathbf{y}(k-2) + 0.5282\mathbf{u}(k-2) + 0.3503\mathbf{u}(k-3) \tag{28}$$

The simulation model structure of co-design of the networked control system with three loops is illustrated by Fig. 3. Controllers, actuators and sensors choose a Truetime kernel models respectively, the joint design optimization module in Fig.3 contains control parameter model and scheduling parameter model, and acts on the sensors and controllers of three loops, in order to optimize system operating parameters in real time.

The initial value of GPC control parameters: 2 *M* , 20 *P* , 0.1 , quantization weights: 12 3 1, 10, 0.1 ; network parameters: CAN bus network, transmission rate is 800kbps, scheduling algorithm is EDF, reference input signal is step signal, amplitude is 500.

Loop1: initial sampling period 1 *T ms* 10 , size of data packet: 100bits, transmission time: <sup>1</sup>*c m* 100 8 /800000 1 *s* ;

Loop2: initial sampling period 2 *T ms* 10 , size of data packet: 90bits, transmission time: <sup>2</sup> *c ms* 0.9 ;

Predictive Control Applied to Networked Control Systems 81

Co-design N-Co-design

 *<sup>k</sup> ms* , *<sup>k</sup>* 

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 <sup>0</sup>

time (s)

the better performance. The system performance of N-Co-design is better than the Codesign one in terms of the small rise time and faster dynamic response. The main reason is the large amount of computation of GPC, and the system adds the amount of computation after considering Co-design, these all increase the complexity of the system and computation delay of network. So, in the ideal case, the N-Co-design system has the better

**Case 2:** Interference signal network utility is 20%, and network induce delay is 3

is bounded by 0 and 1/2 of sampling period, that is 0~5ms. At this case, the network environment is relatively stable, network-induce delay is relatively small, interference signal

Network scheduling timing diagrams of the two algorithms are shown as Fig. 5 and Fig. 6. From the scheduling time diagrams of Co-design and N-Co-design (Fig.5 and Fig. 6), we can find that data transmission condition are better under two algorithms for loop1 and loop2, there are no data conflict and nonscheduled situation. But for loop3, compared with the codesign system, the N-Co-design shows the worse scheduling performance and more latency situations for data transmission and longer duration (longer than 7ms, sometimes), this greatly decreases the real-time of data transmission. The Co-design system shows the better performance: good real-time of data transmission, no latency situations for data, which corresponds to shorter adjustment time for loop3 in Fig.7. The system response curves are

Fig.7 shows that when the changes of network induce delay are relatively small, the response curves of co-design system and N-Co-design system are basically consistency, all three loops can guarantee the system performance. The system performance of N-Co-design is better than the Co-design one in terms of the small rise time and faster dynamic response.

100

occupied relatively small bandwidth.

Fig. 4. The system response

performance.

shown in Fig. 7.

200

300

rev ( rad / s )

400

500

2 1

3

600

700

Loop3: initial sampling period 3 *T ms* 10 , size of data packet: 80bits, transmission time: <sup>3</sup> *c ms* 0.8 .

Fig. 3. Simulation framework of NCS with three loops

## **5.2 Simulation experimental results and their analyses**

The following is comparison of joint design and no joint design, in order to facilitate comparison and analysis, defining as follows: "Co-design" expresses the simulation curve of joint design, while "N-Co-design" expresses the no joint design. Network induce delay can be achieved by delay parameter "exectime" in Truetime simulation. Node 1, 2 and 3 indicate the actuator, controller and sensor in loop 1 respectively; Node 4, 5 and 6 indicate the actuator, controller and sensor in loop 2 respectively; Node 7, 8 and 9 indicate the actuator, controller and sensor in loop 3 respectively.

**Case 1:** In the absence of interfering signals, and network induce delay is 0 *<sup>k</sup> ms* , under ideal conditions, the system response curves of both algorithms are shown in fig.4, where number 1, 2, 3 denote the three loops respectively.

From Fig. 4, in the situation of without interference and delay, the system response curves of Co-design and N-Co-design system response curves are basically consistency; they all show

Fig. 4. The system response

80 Frontiers of Model Predictive Control

Loop3: initial sampling period 3 *T ms* 10 , size of data packet: 80bits, transmission time:

Actuator 1 DC

Actuator 2 DC

Actuator 3 DC

Sensor 1

Sensor 2

Sensor 3

Scheduling

Scheduling parameters

Fig. 3. Simulation framework of NCS with three loops

controller and sensor in loop 3 respectively.

number 1, 2, 3 denote the three loops respectively.

**5.2 Simulation experimental results and their analyses** 

The following is comparison of joint design and no joint design, in order to facilitate comparison and analysis, defining as follows: "Co-design" expresses the simulation curve of joint design, while "N-Co-design" expresses the no joint design. Network induce delay can be achieved by delay parameter "exectime" in Truetime simulation. Node 1, 2 and 3 indicate the actuator, controller and sensor in loop 1 respectively; Node 4, 5 and 6 indicate the actuator, controller and sensor in loop 2 respectively; Node 7, 8 and 9 indicate the actuator,

ideal conditions, the system response curves of both algorithms are shown in fig.4, where

From Fig. 4, in the situation of without interference and delay, the system response curves of Co-design and N-Co-design system response curves are basically consistency; they all show

*<sup>k</sup> ms* , under

*y*1

*y*2

y1 *y*3

**Case 1:** In the absence of interfering signals, and network induce delay is 0

Joint design optimization

Network parameters

<sup>3</sup> *c ms* 0.8 .

Controller 2

Controller 1

Controller 3

Control parameters

*r*3

*r*2

*r*1

the better performance. The system performance of N-Co-design is better than the Codesign one in terms of the small rise time and faster dynamic response. The main reason is the large amount of computation of GPC, and the system adds the amount of computation after considering Co-design, these all increase the complexity of the system and computation delay of network. So, in the ideal case, the N-Co-design system has the better performance.

**Case 2:** Interference signal network utility is 20%, and network induce delay is 3 *<sup>k</sup> ms* , *<sup>k</sup>* is bounded by 0 and 1/2 of sampling period, that is 0~5ms. At this case, the network environment is relatively stable, network-induce delay is relatively small, interference signal occupied relatively small bandwidth.

Network scheduling timing diagrams of the two algorithms are shown as Fig. 5 and Fig. 6.

From the scheduling time diagrams of Co-design and N-Co-design (Fig.5 and Fig. 6), we can find that data transmission condition are better under two algorithms for loop1 and loop2, there are no data conflict and nonscheduled situation. But for loop3, compared with the codesign system, the N-Co-design shows the worse scheduling performance and more latency situations for data transmission and longer duration (longer than 7ms, sometimes), this greatly decreases the real-time of data transmission. The Co-design system shows the better performance: good real-time of data transmission, no latency situations for data, which corresponds to shorter adjustment time for loop3 in Fig.7. The system response curves are shown in Fig. 7.

Fig.7 shows that when the changes of network induce delay are relatively small, the response curves of co-design system and N-Co-design system are basically consistency, all three loops can guarantee the system performance. The system performance of N-Co-design is better than the Co-design one in terms of the small rise time and faster dynamic response.

Predictive Control Applied to Networked Control Systems 83

Co-design N-Co-design

 *<sup>k</sup> ms* , *<sup>k</sup>* 

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 <sup>0</sup>

time (s)

The main reason is the large amount of computation of GPC, and the system adds the amount of computation after considering Co-design, these all increase the complexity of the system and computation delay of network. So, in smaller delay or less network load

is smaller than the sampling period 10ms. At this case, the network environment is relatively worse, interference signal occupied relatively big bandwidth, network-induce

Network scheduling timing diagrams of the two algorithms are shown as Fig. 8 and Fig. 9. From the two situations (Figure 8 and Figure 9) we can see that the data transmission condition of Co-design system is better than the N-Co-design one with all the three loops. Although there are no data conflictions and nonscheduled situation, the N-Co-design system shows the worse scheduling performance and more situations of latency data, which greatly affect the real-time data. This is bad for the real-time networked control system. In contrast, the Co-design system is better, latency data is the less, which can achieve the

As shown in system response curves (Fig. 10) and scheduling timing diagrams (Fig. 8 and Fig. 9), when the network induce delay is bigger, the three loops of Co-design denote the better control and scheduling performance: better dynamic response, smaller overshoot, less fluctuation; scheduling performance guarantees the network induce delay no more than the sampling period, data transfer in an orderly manner, no nonscheduled situation. So, under the case of worse network environment and bigger network induce delay, the system with co-design expresses the better performance, while the worse performance of the system of N-Co-design. The main reason is the operation of control algorithm of Co-design with

**Case 3**: Interference signal network utility is 40%, and network induce delay is 8

100

Fig. 7. The system response

delay is relatively big.

200

300

rev (rad/s)

400

500

2

1

situations, the N-Co-design system has the better performance.

performance of effectiveness and real-time for the data transmission.

3

600

700

Fig. 5. The network scheduling time order chart of N-Co-design

Fig. 6. The network scheduling time order chart of Co-design

Fig. 7. The system response

82 Frontiers of Model Predictive Control

0 0.01 0.02 0.03 0.04 0.05 0.06

0 0.01 0.02 0.03 0.04 0.05 0.06

time (s)

time (s)

Fig. 5. The network scheduling time order chart of N-Co-design

Fig. 6. The network scheduling time order chart of Co-design

1

1

2

3

4

5

6

7

8

9

10

node 9 node 8 node 7 node 6 node 5 node 4 node 3 node 2 node 1 time coordinate

2

3

4

5

6

7

8

9

10

node 9 node 8 node 7 node 6 node 5 node 4 node 3 node 2 node 1 time coordinate

> The main reason is the large amount of computation of GPC, and the system adds the amount of computation after considering Co-design, these all increase the complexity of the system and computation delay of network. So, in smaller delay or less network load situations, the N-Co-design system has the better performance.

> **Case 3**: Interference signal network utility is 40%, and network induce delay is 8 *<sup>k</sup> ms* , *<sup>k</sup>* is smaller than the sampling period 10ms. At this case, the network environment is relatively worse, interference signal occupied relatively big bandwidth, network-induce delay is relatively big.

Network scheduling timing diagrams of the two algorithms are shown as Fig. 8 and Fig. 9.

From the two situations (Figure 8 and Figure 9) we can see that the data transmission condition of Co-design system is better than the N-Co-design one with all the three loops. Although there are no data conflictions and nonscheduled situation, the N-Co-design system shows the worse scheduling performance and more situations of latency data, which greatly affect the real-time data. This is bad for the real-time networked control system. In contrast, the Co-design system is better, latency data is the less, which can achieve the performance of effectiveness and real-time for the data transmission.

As shown in system response curves (Fig. 10) and scheduling timing diagrams (Fig. 8 and Fig. 9), when the network induce delay is bigger, the three loops of Co-design denote the better control and scheduling performance: better dynamic response, smaller overshoot, less fluctuation; scheduling performance guarantees the network induce delay no more than the sampling period, data transfer in an orderly manner, no nonscheduled situation. So, under the case of worse network environment and bigger network induce delay, the system with co-design expresses the better performance, while the worse performance of the system of N-Co-design. The main reason is the operation of control algorithm of Co-design with

Predictive Control Applied to Networked Control Systems 85

considering the effect of network. When the network impact increases, the effect is

**Case 4**: To illustrate the superiority and robustness of the designed algorithm, we add interference to the system at the instant t=0.5s, that is increasing the network load suddenly, the network utility of interference increases from 0 to 40%. The system response curves of

From the system response curves, we can see that the system of Co-design shows the better robustness and faster dynamic performance when increasing interference signal suddenly. In loop 1 (Fig. 11), the system pulse amplitude of Co-design is small, the rotational speed amplitude is 580rad/s (about 5400 cycles/min), the rotational speed amplitude of N-Codesign is nearly 620 rad/s; in loop 2 (Fig. 12), the system amplitude and dynamic response time increase compared to loop 1, but the both can guarantee the normal operation of system; but in loop 3 (Fig. 13), the system occurs bigger amplitude (nearly 660 rad/s) and longer fluctuation of N-Co-design system after adding interference signal, and also the slower dynamic response. The system of Co-design shows the better performance and

From the four cases above, we can conclude that under the condition of better network environment, the system performance of Co-design is worse than the one without Codesign, this is because the former adopts GPC algorithm, and GPC occupies the bigger calculation time, it further increases the complexity of the algorithm with joint design optimization. So, under the ideal and small delay condition, the system without Co-design is better, contrarily, the Co-design is better. When adding interference signal suddenly, the system with Co-design shows the better network anti-jamming capability and robustness.

Fig. 10. The system response

decreased on the control algorithm.

guarantees the stable operation of system.

the three loops with the two algorithms are shown as follows.

Fig. 8. The network scheduling time order chart of N-Co-design

Fig. 9. The network scheduling time order chart of Co-design

84 Frontiers of Model Predictive Control

0 0.01 0.02 0.03 0.04 0.05 0.06

0 0.01 0.02 0.03 0.04 0.05 0.06

time (s)

time s ( )

Fig. 8. The network scheduling time order chart of N-Co-design

Fig. 9. The network scheduling time order chart of Co-design

1

1

2

3

4

5

6

7

8

9

10

node 9 node 8 node 7 node 6 node 5 node 4 node 3 node 2 node 1 time coordinate

2

3

4

5

6

7

8

9

10

node 9 node 8 node 7 node 6 node 5 node 4 node 3 node 2 node 1 time coordinate

Fig. 10. The system response

considering the effect of network. When the network impact increases, the effect is decreased on the control algorithm.

**Case 4**: To illustrate the superiority and robustness of the designed algorithm, we add interference to the system at the instant t=0.5s, that is increasing the network load suddenly, the network utility of interference increases from 0 to 40%. The system response curves of the three loops with the two algorithms are shown as follows.

From the system response curves, we can see that the system of Co-design shows the better robustness and faster dynamic performance when increasing interference signal suddenly. In loop 1 (Fig. 11), the system pulse amplitude of Co-design is small, the rotational speed amplitude is 580rad/s (about 5400 cycles/min), the rotational speed amplitude of N-Codesign is nearly 620 rad/s; in loop 2 (Fig. 12), the system amplitude and dynamic response time increase compared to loop 1, but the both can guarantee the normal operation of system; but in loop 3 (Fig. 13), the system occurs bigger amplitude (nearly 660 rad/s) and longer fluctuation of N-Co-design system after adding interference signal, and also the slower dynamic response. The system of Co-design shows the better performance and guarantees the stable operation of system.

From the four cases above, we can conclude that under the condition of better network environment, the system performance of Co-design is worse than the one without Codesign, this is because the former adopts GPC algorithm, and GPC occupies the bigger calculation time, it further increases the complexity of the algorithm with joint design optimization. So, under the ideal and small delay condition, the system without Co-design is better, contrarily, the Co-design is better. When adding interference signal suddenly, the system with Co-design shows the better network anti-jamming capability and robustness.

Predictive Control Applied to Networked Control Systems 87

Co-design N-Co-design

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

time (s)

First introducing the theory and parameters of GPC , then the EDF scheduling algorithm and parameter are presented. The co-design of control and scheduling is proposed after analyzing the relationship between predictive control parameters and scheduling parameters for a three-loop DC servo motor control system. By analyzing the effect on system performance by the control parameters and the scheduling parameters, a joint optimization method is designed considering the balance between control performance and scheduling performance. Finally this algorithm is validated by Truetime simulation, in the cases of big delay and bad environment, especially the presence of external interference, the co-design system shows the better performance, such as good robustness and anti-jamming

This work is supported in part by National Natural Science Foundation of China (NSFC)

Gaid M B,Cela A,Hamam Y. (2006). Optimal integrated control and scheduling of systems

Gaid M B, Cela A, Hamam Y. (2006). Optimal integrated control and scheduling of

with communication constraints, *Proceedings of the Joint 44th IEEE Conference on Decision and Control and European Control Conference*, pp. 854-859, ISBN 0-7803-9567-

networked control systems with communication constraints: application to a car

0

**6. Conclusion** 

capability.

**7. Acknowledgment** 

under Grant No.60872012

0, Seville, Spain. December, 2005

**8. References** 

Fig. 13. The system response of Loop 3

100

200

300

rev ( rad / s )

400

500

600

700

Fig. 11. The system response of Loop 1

Fig. 12. The system response of Loop 2

Fig. 13. The system response of Loop 3
