7.1 Conclusions
Many research work on modifying the relay feedback auto-tuning method have been reported in recent years. Still there is much room for further improvement and extensions of such methods.
In this thesis, several new results are obtained that improve the accuracy of identification, relay analysis, auto-tuning and cascade control. Briefly, the results are summarized as follows:
A. Identification of linear processes from the half limit cycle data
A class of processes with time delay is analyzed under relay feedback. The time-domain based explicit expressions for output limit cycle waveform are derived to identify the unknown process model parameters accurately. The method acquires more information about the process dynamics from only half limit cycle data. The procedure is not only simple but also obtains the process model parameters without solving any nonlinear equation or optimization problem unlike many relay based methods reported in the literature.
B. Identification of nonlinear processes with monotonic static gains
Apart from linear processes, the relay feedback approach can also be used for identifying nonlinear processes having static nonlinear gain. The extended approach can be used success- fully to estimate the structure of nonlinear model and its parameters from a single symmetrical relay test. The analysis of a limit cycle waveform is shown by considering a hysteresis in the relay test, which may prevent the relay control from oscillating at high frequency and relay switching at wrong instants. The real-time laboratory experiment shows the practical applica- bility of the proposed method.
C. On-line relay auto-tuning for stable processes
The on-line relay method is presented to remove the effects of static load disturbances by the continuous action of the integral controller in the loop. The procedure allows the relay auto- tuning under tight continuous closed-loop control and estimates the process dynamics from the measured half cycle output. The PI controller can then be tuned based on the parametric model such that it preserves the actuator from the large variation of control signals and gives robustness with respect to process parameter variations. The application of a DC servo position control is experimentally tested by the proposed method. The experiment time for the auto-tuning test and performance of the transient response with less control signal variation prove its effectiveness.
D. On-line identification of cascade control systems based on half limit cycle data
The on-line relay method is extended for the auto-tuning of the cascade control system. The time-domain analysis for half cycle outputs is given to estimate the process model parameters.
The approach reduces the time required for the relay test by simultaneously identifying both the inner and outer process dynamics. The improved results of the procedure is also proved with respect to measurement noise and process perturbation.
E. Extension of relay feedback technique for unstable processes with large time delay The necessary condition for the existence of a limit cycle, when a relay with hysteresis test is performed, is developed. A simple control strategy using an inner PD loop is given with a suitable choice of PD gains such that the relay test produces a sustained oscillation for unstable processes with large time delay. The method not only stabilizes relay control systems for the normalize time delay up to 1.95 but also estimates the model parameters accurately.
7.2 Suggestions for Further Work
Following the design methods described in this thesis, a number of possible directions for ex- tensions to this work are discussed below:
• It is natural and interesting at this point to see if the proposed relay analysis can be ex- tended to other class of processes like underdamped and nonminimum phase. In addition, the limit cycle analysis with residual motion is important to be addressed in the design aspect.
• In the presented work, a relay with hysteresis is considered to overcome the problem due to measurement noise in a relay control system. Again the measured noisy limit cycle is successfully denoised using the described filtering technique. The results may be improved by inserting a low-pass filter in the feedback path. The analysis of the relay feedback together with the filter dynamics needs further investigation.
• The relay method is used to identify nonlinear processes with static nonlinearity. Study of nonlinear processes with other kind of nonlinearities such as discontinuous, dead zone and memory type, will be an interesting and useful area of research.
• It will be interesting if a general method for the on-line automatic tuning of stable, inte- grating and unstable processes can be proposed.
• Using the proposed on-line approach for the series cascade structure, the analysis for the parallel cascade structure may be carried out.
• There has been some work in the thesis about the existence and stability of limit cycles for unstable processes in relay feedback systems. Similar investigations may be carried out for processes with more than one integrator.
• Exact analytical methods for identification may be carried out for a multivariable system.