PID Controller Design in Networked Control Systems

This is the M.Sc. thesis of Mr. Mikael Pohjola, graduated in 2006


Introduction

As the use of Internet grows rapidly, new applications, such as networked control systems (NCS), have emerged. Control theory is extending to new areas. The idea to distribute control loops over the Internet, has emerged and this direction is researched widely. The traditional local control loop is expected to expand to tomorrow’s control over large communication networks. The problem is that the network induces a varying time-delay into the control loop, which has to be taken into account in the control design. Conventional control design can not take the varying time-delay into account, new methods are called upon. Simple controllers and tuning rules for these types of systems are needed. The problem is difficult because the time-delay in NCS often has a stochastic nature and it is therefore complicated to approach it analytically. This thesis presents a controller optimisation tuning method for NCS using simulation.

The thesis consists of two parts:

  1. Discrete-time PID controller tuning for varying time-delay systems, including NCS, and
  2. Development of the MoCoNet system.

The controller design in the thesis focuses on an optimisation by simulation tuning technique. The tuning is tested on a real process with the MoCoNet system.

NCS - Networked Control System

In distributed systems or so called Networked Control Systems the controller and the process are physically separate and connected with a network. The measurement and control signals are sent over the network as seen in the figure below, where a fully-distributed NCS is shown. There are two network induced varying time-delays in the control loop. One from the controller to the actuator and one from the sensor to the controller.

Fully distributed NCS

Optimisation Tuning by Simulation

A PID controller structure is selected as the controller for the NCS, as it is easy and intuitive to tune. It is also used extensively in the industry and there is a benefit of using a well-known and trusted controller in future applications. The controller parameters Kp, Ti and Td (in equations below) must be tuned for the controller to perform welltask. Selecting a PID controller is a simple and desirable solution, since it does not require new control algorithms, just new tunings to fit for the varying delay. With a more complex controller the delay could be explicitly taken into account in the control algorithm, and better results could be possible. Despite the simplicity of the PID controller, adequate performance is still achieved.

Discrete-time PID Controller

In the optimisation tuning method the tuning of the controller is based on an optimisation criterion. The optimal tuning parameters are where the criterion or cost function, J, has its minimum. The criterion under optimisation can be any measure of the system performance that depends on the controller tuning. A well known and used criterion is the ITAE criterion shown below. Because of the random time-delay many (n) step response tests are performed and the cost is averaged. This restrains the method from optimising for a certain instance of the varying time-delay.

ITAE cost function

The optimisation tuning method is compared to other traditional methods, such as Ziegler-Nichols frequency and step response test methods and the IMC method.

MoCoNet - Monitoring and Controlling a Laboratory Process over Internet

The MoCoNet system enables students to conduct remote laboratory experiments over the Internet. The interface is an applet and can be run with any Java enabled browser from school or home. The MoCoNet system supports rapid control prototyping (RPC), where controllers built with MATLAB/Simulink can be easily tested on a real process. With a network simulator control design for NCS can be investigated in the MoCoNet system with a real process. Simulation results done in the thesis are verified on the MoCoNet system.

MoCoNet

The MoCoNet GUI

The user interface is shown in the figure above. The control loop is displayed and several setup parameters, such as: reference signal, controller and controller parameters (controller tuning) and network type, may be selected for a run. The process is started with a button click.

Results

Several simulation results are given in the thesis. Optimisation was done for first-order systems with several types of varying time-delay. The results are given as functions of process time constant and controller sampling time. As an example, the results for a NCS with internet delay is shown below. From left to right, top to bottom: the P, I and D parameters for the optimal controller tuning and the cost for the optimal tuning.

Example of optimisation result

The graphs above shows typical tuning behaviour for NCS. One general result was that with increasing sampling time (h) the P and I terms decrease. With increasing process time constant (T) the P and D terms increase.

The tuning was also done for a real example process. The optimisation tuning cost as a function of sampling time showed (below) that there is a local minimum at a relatively long sampling time where the performance of the controller is good. The favourable sampling time is such that the resulting effective delay varies between two values.

Optimisation cost as a function of sample time

A test run on the MoCoNet system demonstrates that the tuning works in practice also.

Test run with MoCoNet

Comparing the optimisation tuning method with the Ziegler-Nichols frequency and step response test methods and the IMC method leads to the conclusion that the optimisation method yields the best results.

Conclusions

The MoCoNet system was developed to enable RCP for educational use in laboratory courses. With the addition of a network simulator, testing of networked control systems was made possible. The MoCoNet system is operational and will be used in the laboratory course at the Control Engineering Laboratory at Helsinki University of Technology.

A general study of optimal tuning for varying time-delay systems was conducted. The results gave rules of thumbs to tune the PID controller for different types of varying time-delays. The tuning results of different varying time-delays were compared to the constant delay case. Differences in the optimal tuning with different types of time-delays were found. However, the optimal tuning for a random delay with a small variance is virtually the same as in the constant delay case.

The optimisation method was applied on networked control systems, where the varying time-delay was a model of the delay in Internet. Several tuning methods were tested on an example process in simulations. Results were also verified on a real process with the MoCoNet system. The optimisation tuning performed better than all the other tuning methods.

The thesis showed that a PID controller can be used to control a process with varying time-delay (Networked control systems), as long as the variation in the delay is small, in the order of the sampling time. Traditional tuning methods, such as Ziegler-Nichols, do not perform well in the new setting of networked control systems. The tuning can instead be done with the optimisation tuning method using simulation described in this thesis.