Research of Network Closed-loop Control System Based on the Model Predictive Control

Delay has a lot of influence on real-time, accuracy and stability performance of the remote control system. Kinetic of equation a single-link robotic arm second-order remote control system as follows[6]:d2ϕdt2=−10sin⁡ϕ−2dϕdt+u

Among them, ^φrepresent the angle of robot arm; ^μ represent the behalf of DC motor torque. simulink block diagram of Mechanical Arm shown in Figure 1.

Figure 1.

Since the forward channel and feedback channel in remote control system is generally the same physical link, the article assumes that the forward channel and feedback channel delay values equal. First set the delay time Delay to 0, that is without delay, adjust the PID parameters (how much) to get the response curve satisfied. Secondly, to maintain the constant of the PID parameters, increase the network delay value gradually when the network delay value is set to 0.02s to get feedback curve in Figure 2 (a), the performance of the system compared with without delay gradual deterioration this time, when the network latency increased to 0.05s, the feedback curve in Figure 2 (b), system becomes a oscillation system, and continue to increase the delay to 0.06s, the feedback curve in Figure 2 (c), system response divergence, that is system becomes unstable. It can be seen that increase the delay gradually make the control systems become increasingly unstable.

Figure 2.

There are a lot of research on the stability improvement of the remote control system, in 1965, Ferrel put forward network delay problem of need to pay attention to time-varying in the network control [7]. Halevi and Ray in the literature[8] augmented deterministic discrete-time model for the periodic network delay, Gregory C. Walsh in the literature[9] considered controller and controlled object is nonlinear time-varying assuming no observation noise, based on nonlinear perturbation method theory, the network delay impact the system is described as a perturbation of the continuous-time systems. Walsh and Bushnel in the literature [10] to prove this method and conclusions can applicable equally to linear systems. Goktas in the literature [11] saw τ_sc and τ_ca as a multiplicative uncertainty bounded perturbation and provided the method of use robust control theory design of NCS controller in frequency domain. Studied robust passive control problem of class of long delay networked control systems in the literature [12], and derive the passive controller design method and proved the validity of the method through simulation. Short delay network control system disturbs by white noise in the literature[13], transformed impact of the random delay on the system into the unknown bounded uncertainties using robust control theory give the H₂/H_∞ system state observer design method. Literature[14] make delay uncertainty convert to the perturbation of the closed-loop system parameters, propose the conditions for the existence of robust guaranteed cost control law based on the robust control theory and Lyapunov stability principle, and gives the method of design of network control Robust guaranteed cost state feedback controller to solve linear matrix inequality. Research show that actually adjust the controller parameters PID makes the instability of the closed-loop control system becomes stable and meet the requirements of remote control system which need less real-time demand. Modify PID parameters of the control system and set the network delay to 0.06s again get feedback curve shown in Figure 3. Research show that modify the PID control parameters has indeed improved the stability of the control system.

Figure 3.

The adjustments of the PID control parameters need to be dynamic adjustment constantly with the size of the control system delay and values and other parameters of systems, which makes controlled object in the work environment unknown to dynamically adapt adjust PID values become remote intelligent control systems that are experiencing another problem. This paper based on the method of modify the control parameters of PID values to improve the stability of the remote control system, and propose intelligent remote control system design methods with adaptive function under a random delay based on neural network theory.

For a module description of the alleged object behavior in the predictive control based on neural network belong to forward model of system, there use the training methods as shown in Figure 4, where dashed box picture shows the actual controlled object, here is the simulink block diagram of the robotic arm, at random input signal u to produce output y. Selected BP neural network with one hidden layer as training model of a controlled object, set the number of hidden layer neurons is 10, using the Levenberg-Marquartdt learning rules, with the group [u, y] data training neural network model of the charged object, the results shown in Figure 5, where Figure 5 (a) is the data used for training, Figure 5 (b) is convergence diagram for training [18].

Figure 4.

Figure 5.

Rolling optimization is an optimal control algorithm, which uses the output of the rolling finite domain optimization that is the goal of optimization over time. Predictive control proposes optimization index based on the moment in every time instead of using global optimization indexes. Rolling optimization index locality through make it can only get the global optimal solution in the ideal case, but when the model mismatch or time-varying and non-linear or confounding factors can take into account this uncertainty in a timely manner compensate, reducing the deviation, keeping the actual optimal control, and it is also easy to use input/output value of finite difference time domain to identify rapidly the state of controlled object so as to implement the online adjustment to the control law and need for repeated optimization.

Optimization algorithm in this article also uses neural network to achieve, set the time-domain involved in the optimization value of 2, using the BP network neural of hidden layer neuron number 7, the same learning rule Levenberg-Marquartdt do the online training to achieve the control signal to the continuous optimization. Training block diagram is shown in the dashed box in Figure 4. Neural network optimization device in accordance with a given input signal u produce predictable output u1, u1 is imposed to the neural network model of the controlled object to produce predictable output y1, y1 compare with the desired output u of the system, and both the difference to train the neural network optimization. Then, the output u2 of the e2 enough litter as the actual amount of control applied to the actual controlled object. Visible, the optimizer in the regulation system is the inverse model of the charged object. Y1 can also be compared with actual output y2, and the error e1 and the actual input u2 of charged object, output y2 as the data of training charged object neural network model.

Feedback correction is forecast control to keep the dynamic correction forecasting model to ensure that the prediction model with infinitely close to the actual controlled object, and make optimization algorithm establish on the basis of the correct prediction of the system state then the new optimization. Error e1 in Figure 6 is the amendment process of the neural network model of the controlled object. Neural network prediction model is built on the basis of the past run data in system, the new operating environment and the actual system has the nonlinear, time-varying, interference and other factors make prediction model based on neural networks need to constantly learn to modify their weights and even structure to ensure that it can well represent the actual controlled object to a control signal prediction.

Figure 6.

Build the Simulation block diagram shown in Figure 6 under robotic arm Smulink environment, network training based on neural network predictive control by the steps in Figure 4-Figure 5, and at the role of the same random input signal gradually adjust the value of delay to simulation. The results in Figure 7 show that the prediction control based on neural network has a good control performance to the fixed delay network. Further used random delay module shown in Figure 8(a) instead of fixed delay module in Figure 5 immediately delay module for delay characteristics of input shown in Figure 8 (b), where In.mat file stored random input signal in Figure 5. There are used random input signal stored in this file in order to compare the simulation results in the simulation. Finally, simulation under the random delay conditions and results shows in Figure 8 (c). Whether a fixed delay or random delay neural network predictive controller can satisfy the closed-loop control requirements in the network delay conditions.

Figure 7.

Figure 8.