Tuning of PID Controllers

There are several approaches that can be used to tune PID controllers, including model-based correlations, response specifications, and frequency response (Smith and Corripio 1985 Stephanopoulos 1984). An approach that has received much attention recently is model-based controller design. Model-based control requires a dynamic model of the process the dynamic model can be empirical, such as the popular first-order plus time delay model, or it can be a physical model. The selection of the controller parameters Kc, ti, to) is based on optimizing the dynamic performance of the system while maintaining closed-loop stability. 

One representation of the dynamic model employs Laplace transforms and is called the transfer function, G s) (Stephanopoulos 1984). 

The process gain is a steady-state characteristic of the process and is simply the ratio, Ay/Ap. The time delay, 9, is the time elapsed before Ay deviates from zero. The time constant is indicative of the speed of response the time to reach 63% of the final response is equal to 6 + t. Graphical analysis of the step response can be employed to compute good estimates of 9 and t when the response deviates from the simplified model. Table 9.4 lists one popular correlation of P, PI, and PID controllers (Stephanopoulos 1984), based on the 1953 work of Cohen and Coon using the 1/4 decay ratio. 

TABLE 9.5 Tuning Relations for PID Controller Based on ITAE Performance Criterion  

Y = KKc for proportional mode, tIt, for integral mode, and tqIt for derivative mode. 9, r are the time delay and time constant based on the process reaction curve, respectively. 

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PID controller is a flexible, effective, and rehable controller for the process industries. A considerable range of controller actions is possible by selecting tuning parameters to provide different weights to the present (proportional), the past (integral), and the projected future (derivative). References related to the tuning of PID controllers are available (20—24). 

K. J. Astrom and T. Automatic Tuning of PID Controllers, Instmment Society of America, Research Triangle Park, N.C., 1987. 

Most chemical processes exhibit stable open-loop behavior. However, there are some important processes, such as chemical and biological reactors, that might be operated around an unstable steady state. The tuning of PID controller forunstable systems has recently attracted attention [16-19], Lee et al. [18] have presented a powerful IMC-based tuning methodology that appears to surpass most of available tuning techniques for unstable systems with low order dy-... 

On-Line Tuning. The model-based tuning of PID controllers presumes that the model is accurate thus these settings are only a first estimate of the best parameters for an actual operating process. Minor on-line adjustments of K, t/, and td are usually required. However, often it is necessary to completely retune the controller after it is put into service, using a trial and error approach. A typical procedure recommended by instrument manufacturers is as follows ... 

Rice, R. and Cooper, D.J. (2002) Design and tuning of PID controllers for integrating (non-self regulating) processes. Procedures of the ISA 2002 Annual Meeting. 

The relay feedback experiment was made popular in the field of process control by Astrom and Hagglund (1984). This experiment was suggested as a means to automate the Ziegler-Nichols scheme for determining ultimate gain and frequency information about a process. Their approach followed directly from a describing function approximation (DFA) to the nonlinear relay element. The objective was to use the obtained process information for automatic tuning of PID controllers. 

Schei, T.S. (1994), Automatic tuning of PID controllers based on transfer function estimation , Automatica 30, 1983-1989. 

The modern DDC controller has only the control function PID. PLC controllers used in process installations may contain more complex regulation functions, for example, the fuzzy or auto-tuning of PID functions. Most DDC controllers are self-sufficient and independent of the controllers or computer programs that are used for system configuration. 

In the present study, we propose a tuning method for PID controllers and apply the method to control the PBL process in LG chemicals Co. located in Yeochun. In the tuning method proposed in the present work, we first find the approximated process model after each batch by a closed-loop Identification method using operating data and then compute optimum tuning parameters of PID controllers based on GA (Genetic Algorithm) method. 

Proportional gain, integral and derivative time constants of PID controllers. Experimental analog of the s = jco substitution calculation. Not necessarily feasible with chemical systems in practice. Tuning relations allow for choices from 1/4 decay ratio to little oscillations. 

Figure 13.6 compares the typical response of P, PI, and PID controllers against the step change of a set-point. As can be seen, a well-tuned PID controller realizes Table 13.2 Determination of parameters of PID control by ultimate gain method. 

This paper presents a general mathematical programming formulation the can be used to obtain customized tuning for PID controllers. A reformulation of the initial NLP problem is presented that transforms the nonlinear formulation to a linear one. In the cases where the objective function is convex then the resulting formulation can be solved easily to global optimality. The usefulness of the proposed formulation is demonstrated in five case studies where some of the most commonly used models in the process industry are employed. It was shown that the proposed methodology offers closed loop performance that is comparable to the one... 

P. Vega, P. Prada, and V. Aleixandre. Self-tuning predictive PID controller. In Proceeding of Inst. Electrical Engineering, pages 303-308, 1991. 

Existing literature on the control of reactor-external heat-exchanger processes is relatively scarce, concerning mostly the implementation of linear (Ali and Alhumaizi 2000, Henderson and Cornejo 1989) and nonlinear (Dadebo et al. 1997) control structures on specific processes. These studies report several control challenges, including difficult tuning of PID and model-based controllers due to the ill-conditioning of the process model. 

A rule based approach to process control has for many years provided an alternative to traditional methods in the form of fuzzy logic control (8,9). Since the advent of expert systems, rulebases have been used for fault diagnosis [10], to advise operators (11) 9 to aid control engineers when installing PID controllers (12), to provide expert on-line tuning for PID controllers (13), and to control processes without the use of fuzzy logic (14,15). 

The PID controller is the most commonly used feedback controller in industry, with three tunable parameters as stated previously. The integral component ensures that the tracking error, E t), is asymptotically reduced to zero, whereas the derivative component imparts a predictive capability, potentially enhancing the performance. Despite its apparent simplicity, the subject of PID controller tuning has been discussed in several textbooks and thousands of research papers since the landmark work of Ziegler and Nichols (1942). In practice, despite these developments, most PID controllers are tuned as PI controllers for several reasons. 

Using Matlab simulates and develops a tuning parameter, model validity in case study This paper is arranged as the following part 2, History review of PID controller tuning techniques. In part 3 there is a brief introduction to the PROCEL pilot plant, on e model is presented in part 4,in part 5,a discussion. ... 

O Dwyer, A. (2000) A summary of PI and PID controller tuning rules for processes with time delay. IFAC Digital Control Past, Present and Future of PID Control, Terrassa, Spain. 

We need first to check whether dynamic compensation is necessary and, if so, obtain estimates for the tuning constants. The approach, as usual, is to first develop a full understanding of the process dynamics. By steptesting the fuel flow SP (MV) we obtain the dynamic behaviour of the temperature (PV). We may already have these dynamics from steps conducted to tune the PID controller. These dynamics we define as (Kp) , 6 and In... 

The PID controller continues to be the most common type of single-loop feedback regulator used in the process industries. However, the tuning of these controllers is still not widely understood and, in fact, many still operate with their original default settings. Despite this, researchers continue... 

More recent developments in the area of PID controller tuning fall into three categories ... 

When noise is present in the measured process output, any derivative action should be accompanied by a filter. However, the problem is often that, as the time constant of the derivative filter is increased to cope with the measurement noise, the closed-loop performance degrades, requiring re-tuning of the controller parameters. This problem is illustrated using the IMC-PID rules appUed to Process A with fd = 0.67. Figure 7.7 shows the closed-loop responses to a negative unit step load disturbance with a derivative filter time constant equal to O.lrp. Figure 7.8 shows the closed-loop responses... 

Note that the controller parameters for the expanded form are three gains, Kc, Kj, and Kjy, rather than the standard parameters, Kc, t/, and td. The expanded form of PID control is used in MATLAB. This form might appear to be well suited for controller tuning, because each gain independently adjust the influences only one control mode. But the well-established controller tuning relations presented in Chapters 12 and 14 were developed for the series and parallel forms. Thus, there is httle advantage in using the expanded form in Eq. 8-16. 

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