FREQUENCY DOMAIN ADAPTIVE CONTROL WITH RELAY FEEDBACK

Abstract

The relay feedback auto-tuning technique has been commercialized for more than 10 years and it has a number of attractive features. It is a closed-loop method which can keep a process around its operating point. The method needs little a priori knowledge of a process and it is simple and robust. The method has been successful in many process control applications. However, it also has some limitations. For example, the estimation error is significant for some processes and only one critical point is acquired from one test, which is insufficient for designing a tight control system. Due to the limited information on process frequency response obtained from a relay feedback test, the standard relay feedback auto-tuner gives satisfactory performance only for a certain kind of processes. Developing auto-tuners which can identify more and accurate points on the process frequency response and which can provide the desired performance for various process dynamics is in great demand. The thesis thus focuses on: (i) the development of multiple-point process frequency response identification from the relay feedback; and (ii) the development of effective control designs for a large class of processes.

In the development of the identification techniques, the idea is to keep the merits of the standard relay feedback auto-tuning method while obtaining more and accurate points on the process frequency response from a single relay test. It is shown that the signals from a relay test cannot be meaningfully converted to the frequency domain by using FFT directly. To overcome the problem, two identification methods under relay feedback are proposed. In the first method, the process input and output are modified by a decay exponential such that FFT can be applied to the resultant input and output to obtain the multiple points on the process frequency response. In the second method, the process input and output are decomposed into transient and stationary oscillatory parts, FFT and digital integral are then employed to find the process frequency response. To enable the identification from relay feedback under non-zero initial condition and to improve the estimation accuracy under step load disturbance, a parasitic relay is proposed. With the parasitic relay superimposed to the standard relay, multiple points on process frequency response can be identified accurately from a single test using the stationary oscillations of the process input and output. To enable the tuning of model-based controllers, a linear algorithm for converting frequency response to a 2nd-order transfer function-is also presented.

With the multiple points on the process frequency response identified, a tight control can be expected if these points are incorporated into a suitable controller design. A frequency response based controller design method is presented which reshapes these multiple points on the process frequency response to best fit the desired loop response. The simplest controller is chosen among all that meet the specifications and the controller parameters are computed with the least squares method. Load disturbance response improvement is also addressed.

For a long dead-time process, a dead-time compensator such as the Smith Predictor (SP) should be used to gain a better system performance. It is known that the Smith Predictor scheme usually requires an accurate model of the process, which is often found wanting in practice. It is, however, shown that a proper mismatch will yield a better performance over the perfect match case and the reason for it is explained. New methods for the process modelling and the primary controller design are then developed. To improve the performance further, a modified Smith Predictor system structure is also presented.

For an unstable process, the original Internal Model Control (IMC) structure should not be used for control system implementation, since the resultant unstable pole-zero cancellation will cause instability. To overcome the problem while keep the IMC structure advantages, the Partial Internal Model Control (PIMC) scheme is proposed. The unstable process is expressed as the sum of the stable part and the completely unstable part. Only the stable part is used as the internal model so that the compensated process is simply the unstable part of the process. This part is usually of very low-order and can easily be controlled by a PID controller.

Integrating the identification methods for multiple points on process frequency response from relay feedback and the multiple points fitting controller design method, an advanced relay feedback auto-tuner for single loop controllers is developed. For implementation, a real-time control system was constructed with a personal computer, AD/DA card and pilot plants. Extensive simulation and real-time testing have demonstrated the effectiveness of the proposed methods.

For a process whose parameters may change from time to time, an adaptive control scheme will be helpful to maintain a consistent performance. A new continual self-tuning scheme based on a load disturbance response is developed. It can estimate the process frequency response for the possibly changed process from the benign process transients under an unknown step or impulse like load disturbance using FFT and least squares method. The controller is then re-tuned based on the updated process frequency response to adapt to the possible changes in the process.

The results presented in the thesis have practical value. With necessary packaging, the findings in the thesis can be applied to industrial control systems. This has been clearly evidenced by a number of the following up collaborative projects with industry on applications of the results of this thesis to cleanroom control, building automation, molding machine control and chemical process control. These projects are going on and are jointly funded by industrial partners and the National Science and Technology Board of Singapore.