DEVELOPMENTS IN MODEL - REFERENCE ADAPTIVE DIGITAL CONTROL

Abstract

Digital computers are being used for the process control applications for the last three decades. Today, computer controlled systems are available for almost all types of the process industries. The rapid technological developments in digital computing systems, coupled with significant reduction in their cost, have made profound impact on the control strategies in the process plants. The high computational speed together with the large storage capacity possessed by modern digital computers, allows the use of advanced control techniques for the real-time control applications. Presently all new plants, both big and small, are designed to work as a computer controlled system. Out of the different control techniques, the adaptive control offers most significant advantages, and is therefore, being widely used in the process industry. In adaptive control methods, the parameters of the controller are automatically adjusted to compensate for variations in the characteristics of the controlled process. The history of applications of adaptive control in the process industry can be traced back to nineteen sixties. However, early experiences in implementing the adaptive algorithms were frustrating due to inadequate computer hardware and difficulty in implementing the computational theories through software. These techniques became feasible later on with the availability of microprocessors and personal computers at low costs and with high computing power. Researchers in the field of adaptive control have devised and implemented different adaptive control strategies like gain scheduling adaptive control system, model reference adaptive control system, self-tuning regulators and other newer techniques, which out-perform the traditional control algorithms. It has been found that each adaptive control technique has certain advantages and disadvantages, and therefore, its application is restricted. Now the new trend has appeared, in which, different adaptive control techniques are combined to take advantages of \ iv, each one of them. There is necessity and scope of improving the adaptive digital control strategies for making them more suitable for the process industry. The objective in the present work is twofold. Firstly, realizing the need of improvement in adaptive digital control techniques, investigations in the various technical aspects of developments in model reference adaptive digital control techniques like Direct Adaptive Control (DAC), Indirect Adaptive Control (IAC) and Combined Direct and Indirect Adaptive Control (CDIAC) have been carried out. These techniques have been studied and modified with the objective of improving their performances. Simulation-studies have been carried out to test the viability of each modified algorithm. Secondly, in order to test the practical viability of proposed adaptive controllers, an experimental countei—flow heat exchanger (CFHE) process has been developed in the laboratory. The robustness of each one of the modified model reference adaptive control techniques has been tested by the simulationstudy, and then, verified on the experimental set-up of the CFHE process. An experimental set-up with a CFHE as the controlled process has been designed and developed in the laboratory. The CFHE process has been selected because of the fact that it is an extensively used process in the chemical industry. It is itself an energy saving unit in which the by-product, namely the hot water, is reused to heat the other products. It is a non-stationary time-varying single-input single-output (SISO) process and is most suitable for implementing the adaptive control strategies. It is represented mathematically as a first order process. In addition to the CFHE process, the setup consists of associated electronic -hardware circuits, viz. signal-conditioning unit (SCU) for conditioning different temperature signals from the process, electronic ON/OFF temperature controller to control hot water temperature used as the manipulating variable in the present control system, analog-to-digital and digital-to-analog converters to interface iv) the experimental process with a personal computer, voltage-tocurrent converter to convert D/A converter's voltage output into a current signal and current-to-pressure converter to convert the current signal into a corresponding pneumatic (pressure) signal and thus to interface a linear pneumatic control valve with the computer. The dynamics of the springdiaphragm actuator of this control valve is faster than that of the CFHE process, and hence, the dynamics of the actuator is not considered in the control design. In a bid to improve the existing adaptive control techniques, first attempt has been made to modify the adaptive digital PID controller with the use of different combinations of the process identification and controller parameter estimation methods. The process reaction curve method for process identification has been used and the first-order process parameters are identified. Then by using discreteversion of the identified parameters and for the given closedloop system performance, the parameters of the controller are estimated. The proposed method has been tested for the improvement in its set point tracking and robustness against load-disturbance by simulation-study as well by its real-time implementation on the CFHE process. The results obtained are compared with a continuous-time PID controller. The parameters of this controller are based on the Cohen-Coon settings. In all the modified adaptive control techniques, it has been assumed that the plant is a lineal—time-invariant singleinput single-output (LTI SISO) system and strictly proper, the sign of gain is known, the degrees of monic stable denominator polynomial and numerator polynomial of the plant are known, the relative degree of the plant is known and the coefficients of numerator and denominator polynomial are unknown. Further, it is assumed that the reference model is strictly proper transfer function and reference input to the model is uniformly bounded. Then adaptive control problem is to determine a suitable control function such that the tracking error between the plant and model outputs tends to zero. \ vi; Effort has also been made to modify the existing direct model reference adaptive control technique (DAC) to improve its performance. In the existing structure of direct adaptive control, the controller parameters are calculated using the plant output and the reference input only. Thus, in order to get asymptotic tracking of the plant output to the model output, the constant adaptive gains have to be adjusted by trial and error method. In the proposed modification aimed at avoiding this tedious procedure of adjustment, of adaptive gains, additional controller parameters have been generated by using the low pass-filtered signals from the plant input and output. The other advantages are that it relaxes the SPR condition on the plant, gives the tracking error of true difference between the plant and model outputs, satisfies a wider class of processes, eliminates the bias in the steady state, that it is applicable to non-minimum phase plants and that it is robust against time-varying nature of plant, unmodelled dynamics and load disturbances. The improvements in all these characteristics of the proposed DAC have been verified by a simulation study on first, second, and third order process models and as well as by on-line experimental study on the CFHE process. The stability of the overall system is confirmed by constructing a Lyapunov function. Three improved algorithms have been developed for indirect adaptive control, namely, IAC-I, IAC-II and IAC-III. The IAC-I uses the prior information about the plant, i.e. the gain. In IAC-II, the gain is assumed to be unknown and in IAC-III, the adaptive control laws have been modified by using both closedloop estimation errors (CLEE). This leads to a further improvement in IAC-III because use of both CLEEs in controller parameter calculations help in providing more information about the plant. The stability of all these techniques is ensured by the existence of the Lyapunov functions. These IAC techniques have been tested through simulation and experimental study on the CFHE process to observe their setpoint tracking and robustness against lead-disturbance. (.VII The combined direct and indirect adaptive control strategies proposed by earlier workers have been modified to improve their performance. One of them, named here as CDIAC-1, uses an alternative identification model and both CLEEs in the laws of adaptive control. This algorithm has been tested for three cases, namely use of an alternative identification model alone, use of modified control laws alone and use of both of them simultaneously. For several values of plant parameters, the first two modifications show satisfactory response, whereas the third modification gives a significant improvement in the speed of settlement and accuracy for all values. The CDIAC-1 has been tested for set-point tracking, reliable plant identification and robustness against time-varying parameters, and unmodelled dynamics by a simulation study on a different first order process models and real-time experimental study on the CFHE process. In all the cases, it shows a performance superior to that of the original CDIAC. Then another CDIAC for a second-order process has been modified to improve its performance by using low-pass filters at the input and output of the plant. It has been tested for the set point tracking and robustness for a time-varying second-order plant and with large external disturbances. A major modification in CDIAC, named here as CDIAC-2, has been carried out, in which the estimated plant parameters (estimated by using recursive least-square algorithm with variable forgetting factor) along with the reference model parameters are used in controller parameter estimation and the error between the plant and the reference model outputs is used in the control laws. Thus both the plant parameter estimates and the reference model parameters along with output tracking error are used simultaneously. The CDIAC-2 relaxes the assumption on the relative degree of the plant and the model considered by previous researchers. It has been tested for set point tracking and robustness by simulation techniques and by real-time experimentation. Thus CDIAC-2 is the combination of different adaptive control concepts and mechanisms (model (viii, reference adaptive control design, recursive least square identification and variable forgetting factor) in a single framework of an adaptive control algorithm and performs better than all other methods including modified methods. The hardware and control developed for the CFHE process instrumentation works satisfactorily. The dynamics of the actuator of control valve is faster than the dynamics of the process. Thus the performance of tested algorithms was not affected by the dynamics of the control valve. The digital adaptive PID controller developed gave better set point tracking and showed more robustness against disturbances in CFHE process control as compared to continuous-time PID controller based on the Cohen-Coon method. It is observed that in all the cases, the ISEs of the digital PID controller are smaller than those of the continuous time controller. The difference is similar in simulatory and experimental studies. The modified DAC is a simple adaptive controller structure with fewer adjustable parameters and easier to implement for real-time applications. Both the simulation and experimental results show that the modified DAC is stable and robust against the parametric uncertainties and load disturbances. It produces a larger initial control action when set point is changed, which leads to a shorter settling time. Moreover, there are no oscillations in the output, whereas, the original DAC gave oscillatory response. The comparison between three IAC technique has been made in terms of ISEs and it is found that the performance of IAC-I is better than IAC-II. This is due to the fact that in IAC-I, the gain of the process is known which helps in parameter tracking more closely. The ISE observed with ISE-III was the smallest. The CDIAC-1 has smaller ISE than the original CDIAC. This is due to the fact that alternative identification model is very close to the plant under control and use of both the CLEEs in control laws gives more information about the plant. The modified CDIAC for second order process gives satisfactory (ix) tracking response against the large external disturbance and time varying parameters. The CDIAC-2 shows the improved performance in all the process conditions. The combination of stable model reference adaptive control design and a reliable plant identification using recursive least square identification method with variable forgetting factor shows superior performance to any other method presented in the thesis. From the ISEs, it is observed that the CDIAC-2 has a better performance than all other adaptive controllers, whereas, the CDIAC-1 is better than IACs and DACs. The modified DAC has better response than the IACs. It can be concluded that the performance of all the adaptive controllers is superior to that of PID controller. This is obviously due to the fact that the PID controller has fixed parameters, whereas, parameters of adaptive controller change as per the change in the plant dynamics. To sum up, the primary objective of modifying and improving the existing adaptive control schemes and implementing them for real-time process control has been effectively achieved in this thesis. Hopefully, the present work will add to the state of art of digital adaptive control techniques and their implementation.