AUTOTUNING OF MULTIVARIABLE CONTROLLER FROM RELAY FEEDBACK

Abstract

Many industrial processes are inherently of multivariable nature and need multi variable control to enhance performance. There is a strong motivation to derive a simple and effective means for tuning multivariable process controllers. The relay feedback autotuning 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 the process and it is simple and robust. Since the relay auto-tuning of SISO PID controllers has been widely adopted in industries, its extension to the multivariable system is in high demand. This thesis aims to provide some insights into how the dynamic information of multivariable process can be extracted by using the relay feedback technique and how multivariable process controllers, especially multivariable PID-type controllers can be tuned on the basis of such dynamic information. When the relay technique is extended to a MIMO system, there are three possible relay feedback schemes, which are Independent Single Relay Test, Sequential Relay Test and Decentralized Relay Test. Multivariable process identifications from each type of relay feedback are investigated in this thesis. In the first method, a new low-order modeling technique for SISO process from relay steady-state response is developed and extended to model multivariable processes from Independent Single Relay Tests. In the second method, a frequency response identification technique from Sequential Relay Feedback for multivariable process is developed. The transient responses are used and the FFT based frequency response identification technique is developed to obtain the process frequency responses. Simple non-iterative formulas for converting the multiple frequency response points into a low-order plus dead-time model are also derived. As for the most desired tuning test - decentralized relay feedback, two multivariable process identification methods are proposed based on steady-state response and transient response respectively. In the first method, multivariable oscillations under decentralized relay feedback are investigated, some new results on characteristics of relay system are obtained, and they are used to develop a method for identifying the process frequency response matrix at the oscillation frequency based on the steady state response information. A bias is further introduced into the relay to additionally obtain the process steady state matrix. In the second method, the transient responses from the decentralized relay feedback testing are used and the FFT based frequency response identification technique is developed to obtain the process frequency responses. With the frequency response of the multivariable process identified, two frequency response approaches to the tuning of fully cross-coupled multivariable controllers are presented. In the first approach, an objective closed-loop transfer function matrix is specified, and the fully cross-coupled multivariable PID-type controller matrix is determined altogether such that the actual closed-loop performance is best fitted to the desired one by using linear least squares frequency response fitting method. In the second approach, a new set of design equations are derived under the multivariable decoupling conditions where the equivalent diagonal plants are independent of off diagonal elements of the controller and used to design its diagonal elements first. As such, the multivariable process controllers are tuned by solving a set of scalar frequency response fitting problems with linear least square method at two points or multiple frequency points. For processes with modest interactions, multi-loop controllers are often more favored than multivariable fully cross-coupled controllers, as they have much simpler structures and fewer tuning parameters to handle than the fully cross-coupled controllers. A new method for the design of multi-loop PI controllers is developed. The key idea is to make the loop characteristic loci each pass through desired positions in the complex plane so that combined gain and phase margin type of specifications is satisfied with the controller. 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. For multivariable processes with multiple time delays, the existing multivariable Smith Predictor schemes have some drawbacks like the poor performance and design complications. A new approach to the multivariable Smith predictor controller design is developed for better decoupling and loop performance. Based on the process identification methods and the controller design methods developed in this thesis and some co-workers' results, an advanced PID auto-tuner is developed for Heating, Ventilation, and Air-Conditioning (HVAC) systems. The key function of the tuner is auto-tuning of single- or multi-variable controllers to replace the present tedious and poor manual tuning/re-tuning of independent loop PID controllers. It contains two identification methods and two PID design methods. The auto-tuner has been tested on a HVAC pilot plant and a commercial building and the results demonstrate the effectiveness of the auto-tuner. In summary, multi variable process identification and tuning of multivariable process controllers from relay feedback have been developed in this thesis. The results obtained in the thesis have both sound theoretical contributions and useful practical values. The effectiveness of these findings has been demonstrated in extensive simulation and real-time implementations presented in the thesis. With necessary packaging and re-engineering, the findings in the thesis can be applied to industrial control systems.