Based on the T-S model, a predictive compensation scheme including timer and counter for wireless networked system with long time delay and data packet dropout is proposed in this paper. By the separation principle, the state observation predictor and the state feedback controller are designed separately. For the case of fixed delay, the stability of the closed-loop networked control systems is discussed. Simulation by inverted pendulum system illustrates the effectiveness of the proposed method in wireless networked system based on T-S model.

It has always been hot research on how to reduce the network-induced delays, packet dropouts, and other factors that affect the stability of the networked control systems and wireless sensor networks [

The framework of the system over a network medium researched in this paper is shown in Figure

The structure of wireless networked control system.

For convenience, some general assumptions are given as follows.

The node of sensor is time-driven, and the sampling period denoted by

There is no time delay or packet dropout during a sampling period. And assume that the data are lost if the transmission time exceeds the maximum transmission delay, which is set as

The time delay and packet dropout between the sensor and the controller are marked as

The output data from the sensor and the controller have a time stamp and are transmitted with a single packet without wrong order.

Consider a plant described in the following state-space form:

According to [

By using the fuzzy inference method with a singleton fuzzifier, product inference, and center average defuzzifier, we can get the global fuzzy equation of the

In real networked control system, limited by environmental or economic conditions, not all state variables are measurable. Based on hierarchical control structure, the design of networked control system with local state observer is presented in [

Wireless networked system digraph with predictor.

The buffer and memory are used for temporary storage of data, which can filter data and avoid the wrong order. And the main purpose of the counters is to calculate the packet dropout.

Between the sensor and the controller, define two variables,

Similarly, between the controller and the actuator, define two variables,

Networked control system can bear a certain degree of packet dropout. Hence, computing packet dropout rate currently will help ensure the stability of the system. The packet dropout rate

For arbitrary initial value of system (

Assume that the current moment is

As we all know, the packet dropout can also be converted to time delay. Values at current moment cannot be acquired because of the network-induced delay. Even so,

From the above formulas, the relationship between

There exist random delay and packet dropout between the controller and the actuator, marked as

The state feedback controller is designed as formula (

By formulas (

Substituted into the formula (

Construct

Comparing the time stamp with local time or by the counter, we can achieve

With (

Thus, the control law now is

At time

Define the following error vector:

(1) When

Then combined with formula (

By formula (

Therefore,

Then,

Thus, with (

And then, with (

Then, on the basis of formulas (

(2) When

According to (

Therefore,

By formula (

Then with (

As we know, if all the eigenvalues of the matrix

Consider an inverted pendulum system [

Then, set

As a result, the T-S fuzzy model can be written as follows:

By using rank criteria of system controllability and observability, the system is completely controllable and completely observable. Consider

The controller poles are assigned to

The membership functions are chosen from [

Outputs of the wireless networked system in different situations.

Aimed at the wireless networked control systems with random time delay more than a sampling period and packet dropout, in this paper, on the basis of a compensation method in [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China under Grant no. 61374083, Science and Technology Department Project of Zhejiang Province under Grant nos. 2014C31082, 2014C33109, and Program of Graduate Innovation Research in Zhejiang Sci-Tech University (YCX12028).