**4. Process reaction curve**

252 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

Temperature variation in polymerization reactor systems greatly affects the kinetics of polymerization and consequently changes the physical properties and quality characteristics of the produced polymer (Ghasem et al., 2007; Lepore et al., 2007). In order to ensure the maintenance of the final product quality is crucial to keep suitable operating conditions

The PID controller is designed for temperature control of an experimental process of polymerization (Leite et al., 2010a; Leite et al., 2011). The developed models will can be online implemented to a pilot plant. A pilot plant was built specifically to evaluate the polymerization reaction performance. It consists essentially of a stirred batch reactor, an oil storage tank, a positive displacement pump and temperature sensors. Thermal oil was used

Using a PCL (Programable controller logic), a thermal fluid variable speed pump will be driven by the controller, to maintain the temperature constant into the reactor. The flow of thermal fluid (manipulated variable) was step of 30 and 100%. The maximum pump flow rate equivalent to approximately 900 L/H. Disturbances in the manipulated variable were

as heat transfer medium in the jacket. The polymerization reaction is exothermic.

The Figure 3.3 shows response of the experiment using the relay method.

Fig. 3.3. Response of the experiment using the relay method

Table 3.2.

According to the tuning method used, we found the initial control parameters as shown in

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> <sup>0</sup>

**Time (s)**

**Tempo (s)**

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> -2

**Tempo (s)**

**Time (s)**

during the polymerization reaction process.

performed in a short time interval (P=300 s).




0

50

50

0

0

**Vazão do Fluido Térmico (%)**

pump speed (%)

100

100

**Variação de Temperatura (°C**

T (ºC) 0

0

1

3

**3.2 PID controller design** 

The closed-loop system will respond in a desirable way only if its controller is properly tuned. This means that its proportional, integral and derivative (PID) settings are properly made. A popular procedure for tuning a controller is the Ziegler-Nichols Reaction Curve Tuning Method.

This procedure requires a step change of the controllers output alters the controlled variable. The Figure 4.1 shows the resultant closed loop step.

The method used to make the step change and measure the controlled variable is called the Process Identification Procedure. This controller setting puts the system into an open-loop condition. Based on the shape and magnitude of the controlled variable's reaction curve in reference to the step change, value are obtained and used in mathematical formulas. These values are then used to determine the PID settings.

Fig. 4.1. Resultant closed loop step

Loop responses for a unit step reference are shown in Figure 2 (similar to Figure 1). A linearized quantitative version of the model in Equation 3.3 can be obtained with an open loop experiment, using the following procedure:


#### d. Compute the parameter model as follows:

$$K\_0 = \frac{\nu\_{\rm os} - \nu\_0}{u\_{\rm os} - u\_0} \tag{4.1}$$

Relay Methods and Process Reaction Curves: Practical Applications 255

temperature directly affects the final activity of the enzyme precipitated. The use of controllers to maintain the temperature of this process prevents the denaturation of the enzyme, improving the quality of the product. It is also important to emphasize that the design of the developed controllers can be easily extended to similar processes in which

The robust PID controller is designed for temperature control of an experimental process of enzyme recovery from pineapple rind. To assess the performance of the controllers the following parameters were used: ITAE (integral of Time multiplied by Absolute Error), response time, saturation of the final element of control, enzymatic activity of the product

Conventional controller was implemented in experimentally tested in a pilot plant of the

The proteolytic enzyme bromelain (EC 3.4.22.4[\*]) is precipitated with alcohol at low temperature in a fed-batch jacketed tank. Temperature control is crucial to avoid irreversible protein denaturation. Using a Fieldbus network architecture, a coolant variable speed pump

Tuning the controllers proved to be a difficult task in this fed-batch nonlinear process. To tune the controller, by Ziegler and Nichols, a new methodology for the experimental

In order to evaluate the influence of the variation of the tank volume on the precipitation process, and to obtain the process reaction curve samples containing extract and ethanol in different proportions (from 1:1 to 1:3 v/v) were used in the pseudo-steady state operation. Positive and negative disturbances were then applied (± 30%) to the initial conditions of the speed of the coolant pump (manipulated variable). The data obtained from the reaction curve (Figure 4.3) for this process allowed to find initial values of the process parameters Kp

*[\*]The Enzyme Commission number (EC number) is a numerical classification scheme for enzymes, based on the* 

Fig. 4.3. Reaction curves obtained from disturbances in the manipulated variable.

precipitation process (Leite et al., 2010b; Leite et al., 2010c; Silva et al., 2010).

was driven by the controller, to maintain the temperature constant into the tank.

some transient and nonlinear behavior are found.

and electric power consumption of the cooling system.

procedure was designed and implemented (Leite et al., 2010c).

(static gain), τp (time constant) and d (time delay).

**4.2 PID controller design** 

*chemical reactions they catalyze.* 

$$
\tau\_0 = t\_1 - t\_0 \tag{4.2}
$$

$$\mathbf{y}\_0 = \mathbf{t}\_2 - \mathbf{t}\_1 \tag{4.3}$$

*m.s.t stands for maximum slope tangent* 

Fig. 4.2. Reaction curve: Process Identification Procedure

The model obtained can be used to derive various tuning methods for PID controllers. This method was proposed by Ziegler and Nichols. In their proposal the design objective is to achieve a particular damping in the loop response to a step reference.

The parameter setting rules proposed in Table 4.1 are applied to the model (Eq.3.3), where we have again normalized time in delay units.


Table 4.1. Ziegler-Nichols tuning using the reaction curve.

#### **4.1 Case study**

Bromelain is widely used in the chemical and pharmaceutical industries. It is employed not only for its pharmacological effects, but also in food industry activities such as brewing and meat processing (Kelly, 1996). Currently there were no experimental studies about automation and process control in the production of bromelain, despite the growing number of scientific papers related to this enzyme. Temperature control during the recovery process of the bromelain from pineapple fruits is an extremely important practice, because the temperature directly affects the final activity of the enzyme precipitated. The use of controllers to maintain the temperature of this process prevents the denaturation of the enzyme, improving the quality of the product. It is also important to emphasize that the design of the developed controllers can be easily extended to similar processes in which some transient and nonlinear behavior are found.

The robust PID controller is designed for temperature control of an experimental process of enzyme recovery from pineapple rind. To assess the performance of the controllers the following parameters were used: ITAE (integral of Time multiplied by Absolute Error), response time, saturation of the final element of control, enzymatic activity of the product and electric power consumption of the cooling system.

### **4.2 PID controller design**

254 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

�� <sup>=</sup> ����� �����

The model obtained can be used to derive various tuning methods for PID controllers. This method was proposed by Ziegler and Nichols. In their proposal the design objective is to

The parameter setting rules proposed in Table 4.1 are applied to the model (Eq.3.3), where

Bromelain is widely used in the chemical and pharmaceutical industries. It is employed not only for its pharmacological effects, but also in food industry activities such as brewing and meat processing (Kelly, 1996). Currently there were no experimental studies about automation and process control in the production of bromelain, despite the growing number of scientific papers related to this enzyme. Temperature control during the recovery process of the bromelain from pineapple fruits is an extremely important practice, because the

�� <sup>i</sup> <sup>d</sup>

���

��� 0,5τ�

(4.1)

�� = �� � �� (4.2)

�� = �� � �� (4.3)

d. Compute the parameter model as follows:

*m.s.t stands for maximum slope tangent* 

Fig. 4.2. Reaction curve: Process Identification Procedure

we have again normalized time in delay units.

<sup>P</sup>��

PI 0,���

PID �,���

**4.1 Case study** 

achieve a particular damping in the loop response to a step reference.

����

����

����

Table 4.1. Ziegler-Nichols tuning using the reaction curve.

Conventional controller was implemented in experimentally tested in a pilot plant of the precipitation process (Leite et al., 2010b; Leite et al., 2010c; Silva et al., 2010).

The proteolytic enzyme bromelain (EC 3.4.22.4[\*]) is precipitated with alcohol at low temperature in a fed-batch jacketed tank. Temperature control is crucial to avoid irreversible protein denaturation. Using a Fieldbus network architecture, a coolant variable speed pump was driven by the controller, to maintain the temperature constant into the tank.

Tuning the controllers proved to be a difficult task in this fed-batch nonlinear process. To tune the controller, by Ziegler and Nichols, a new methodology for the experimental procedure was designed and implemented (Leite et al., 2010c).

In order to evaluate the influence of the variation of the tank volume on the precipitation process, and to obtain the process reaction curve samples containing extract and ethanol in different proportions (from 1:1 to 1:3 v/v) were used in the pseudo-steady state operation.

Positive and negative disturbances were then applied (± 30%) to the initial conditions of the speed of the coolant pump (manipulated variable). The data obtained from the reaction curve (Figure 4.3) for this process allowed to find initial values of the process parameters Kp (static gain), τp (time constant) and d (time delay).

*[\*]The Enzyme Commission number (EC number) is a numerical classification scheme for enzymes, based on the chemical reactions they catalyze.* 

Fig. 4.3. Reaction curves obtained from disturbances in the manipulated variable.

Relay Methods and Process Reaction Curves: Practical Applications 257

order to keep the overshoot to a minimum, intense controller response is required, causing

Despite the PID1 controller have lower power consumption, the PID controller showed better global performance criteria: small overshoot, small rise time, small ITAE, short

The adaptative PID tuning procedure, based on the analysis of the process reaction curves, can be an attractive strategy to provide a suitable non-linear controller design for transient processes. The further development of the adaptive PID controller can contributed to

PID control tuning are popular and offer many benefits such ease of use, new development help to implement other PID controller variants, and control for common industry

In this chapter, two techniques from PID tuning were applied for the temperature control of the practical applications: 1-polymerization system and 2-bromelain precipitation. The main feature of these process is its complex nonlinear behavior, wich poses a challenging control

In the first case a PID controller experiment was designed to be implemented later in the pilot plant. The controller was developed from the relay method proposed by Astrom and

In the second case the controller was designed based on reaction curve method of Ziegler and Nichols, by disturbances in a real experimental system bromelain precipitation. The authors carried out fine-tuning of this controller, which was subsequently implemented

The methods performed well for estimation of the PID controller, easy to apply and prove to be an effective option in practical cases will help achieve the proposed objectives*.* There is a large number of tuning methods, but related methods cover most practical cases and

Åström, K. J. & Hägglund, T. (2004). Revisiting the Ziegler-Nichols step response method

Ghasem, N. M., Sata, S. A. & Hussain, M. A. (2007). Temperature control of a bech-scale

Kelly, G. S. (1996). Bromelain: A literature review and discussion of its therapeutic

Leite, M. S. ; Fileti, A. M. F. & Silva, F. V. (2010c). Development and experimental

COBEQ, Brazil, Foz do Iguaçu, 2010, Vol. 1, p. 7539-7548., ISSN 2178-3659.

applications. *Alternative Medicine Review*, Vol. 1, No. 4, pp. 243-257.

batch polymerization reactor for polystyrene production. *Chemical Engineering* 

application of fuzzy and conventional controllers to a bioprocess. *Revista Controle & Automação*, Vol. 21, No. 2, March and April 2010, pp. 147-158, ISSN 0103-1759. Leite, M. S.; Fileti, A. M. F. & Silva, F. V. (2010a). Design, assembly and instrumentation of

an experimental prototype for the application of automation techniques and development of control strategies in a polymerization process. Proceedings of XVIII

for PID control. *Journal of Process Control*, Vol. 14, pp. 635-650.

response time and pump saturation time and higher enzyme activity in the product.

improving the performance of the conventional PID controller.

pump saturation.

**5. Conclusions** 

system design for the batch reactor.

common industry applications.

**6. References** 

efficiently in maintaining the process temperature.

*Technology*, Vol. 3, No. 9, pp. 1193-1202.

applications.

Haglund.

Fine tuning was then conducted to adjust these parameters by trial-and-error procedure. In these closed loop experiments, the following indices of performance were considered: ITAE, response time and saturation of the final element of control.

The best parameters found after this fine tuning were: Kc=35%/°C, i = 28s and d = 7s (PID2). Figure 4.4 shows the behavior of the tank temperature under well-tuned conventional PID.

Fig. 4.4. Behavior of the controlled and manipulated variables under PID1 control (Kc=8%/°C, i = 28s e d = 1,5s) and PID2 (Kc=35%/°C, i = 28s e d = 7s).

Table 4.2 presents quantitative and qualitative analyses of the performance of the implemented controllers.


Table 4.2. Performance parameters of the PID controllers.

From these results, it is clear that PID controllers performed satisfactorily in controlling the temperature of the precipitation process. However, the PID2 controller kept the variation closer to the set-point, which is important for enzyme activity recovery, since the enzyme is highly sensitive to temperature changes. The early stage of ethanol addition is critical. In order to keep the overshoot to a minimum, intense controller response is required, causing pump saturation.

Despite the PID1 controller have lower power consumption, the PID controller showed better global performance criteria: small overshoot, small rise time, small ITAE, short response time and pump saturation time and higher enzyme activity in the product.

The adaptative PID tuning procedure, based on the analysis of the process reaction curves, can be an attractive strategy to provide a suitable non-linear controller design for transient processes. The further development of the adaptive PID controller can contributed to improving the performance of the conventional PID controller.
