Unit-1: Process Control Process Control Hardware Fundamentals In order to analyse a control system, the individual components that make up the system must be understood. Only with this understanding can the workings of a control system be fully comprehended. The rest of this book deals extensively with controller and process characteristics. It is therefore appropriate and necessary that hardware fundamentals for the primary elements and final control elements be studied first in this chapter. Discussion of controller hardware is delayed until Chapter 4, where the control equations governing the controllers are covered. Several of the concepts introduced in this chapter are discussed in further detail in later sections of this book. 2.1 Control System Components A control system is comprised of the following components: 1. Primary elements (or sensors/transmitters) 2. Controllers 3. Final control elements (usually control valves) 4. Processes Figure below illustrates a level control system and its components. The level in the tank is read by a level sensor device, which transmits the information on to the controller. The controller compares the level reading with the desired level or set point and then computes a corrective action. The controller output adjusts the control valve, referred to as the final control element. The valve percent opening has been adjusted to correct for any deviations from the set point. controlled variables - these are the variables which quantify the performance or quality of the final product, which are also called output variables. manipulated variables - these input variables are adjusted dynamically to keep the controlled variables at their set-points. disturbance variables - these are also called "load" variables and represent input variables that can cause the controlled variables to deviate from their respective set points.
Control Terminology set-point change - implementing a change in the operating conditions. The set-point signal is changed and the manipulated variable is adjusted appropriately to achieve the new operating conditions. Also called servomechanism (or "servo") control. disturbance change - the process transient behavior when a disturbance enters, also called regulatory control or load change. A control system should be able to return each controlled variable back to its set-point. Illustrative Example: Blending system
Interacting and Non-Interacting Processes Consider two liquid storage tanks in series. They can be arranged in two fashion, viz. interacting and noninteracting. Following figure demonstrates the types of the said arrangements: (a) Interacting Process (b) Non-interacting Process Fig. III.12: Liquid storage tanks arranged in Interacting and Non-interacting fashion In non-interacting arrangement of storage tanks (Fig. III.12b), the level of liquid in tank 2 does not have any effect of that in tank 1, whereas in interacting arrangements of tanks, the levels in both the tanks affect each other. Characteristics of a Process Different processes have different characteristics. But, broadly speaking, there are certain characteristics features those are more or less common to most of the processes. They are: (i) (ii) (iii) The mathematical model of the process is nonlinear in nature. The process model contains the disturbance input The process model contains the time delay term. In general a process may have several input variables and several output variables. But only one or two (at most few) of the input variables are used to control the process. These inputs, used for manipulating the process are called manipulating variables. The other inputs those are left uncontrolled are called disturbances. Few outputs are measured and fed back for comparison with the desired set values. The controller operates based on the error values and gives the command for controlling the manipulating variables. The block diagram of such a closed loop process can be drawn as shown in Fig.
In order to understand the behavour of a process, let us take up a simple open loop process as shown in Fig. It is a tank containing certain liquid with an inflow line fitted with a valve V 1 and an outflow line fitted with another valve V 2. We want to maintain the level of the liquid in the tank; so the measured output variable is the liquid level h. It is evident from Fig.2 that there are two variables, which affect the measured output (henceforth we will call it only output) - the liquid level. These are the throttling of the valves V 1 and V 2. The valve V 1 is in the inlet line, and it is used to vary the inflow rate, depending on the level of the tank. So we can call the inflow rate as the manipulating variable. The outflow rate (or the throttling of the valve V 2 ) also affect the level of the tank, but that is decided by the demand, so not in our hand. We call it a disturbance (or sometimes as load). The major feature of this process is that it has a single input (manipulating variable) and a single output (liquid level). So we call it a Single-Input-Single-Output (SISO) process. We would see afterwards that there are Multiple-Input-Multiple-Output (MIMO) processes also. Mathematical Modeling In order to understand the behaviour of a process, a mathematical description of the dynamic behaviour of the process has to be developed. But unfortunately, the mathematical model of most of the physical processes is nonlinear in nature. On the other hand, most of the tools for analysis, simulation and design of the controllers, assumes, the process dynamics is linear in nature. In order to bridge this gap, the linearization of the nonlinear model is often needed. This linearization is with respect to a particular operating point of the system. In this section we will illustrate the nonlinear mathematical behaviour of a process and the linearization of the model. We will take up the specific example of a simple process described in Fig.2. Let Q i and Q o are the inflow rate and outflow rate (in m 3 /sec) of the tank, and H is the height of the liquid level at any time instant. We assume that the cross sectional area of the tank be A. In a steady state, both Q i and Q o are same, and the height H of the tank will be constant. But when they are unequal, we can write,
Q Q = A dh (1) i o dt But the outflow rate Q o is dependent on the height of the tank. Considering the Valve V 2 as an orifice, we can write, (please refer eqn.(4) in Lesson 7 for details) Q o = C d A 2 2g (P1 P 2 ) (2) 1 β 4 γ We can also assume that the outlet pressure P 2 =0 (atmospheric pressure) and P 1 = ρ gh (3) Considering that the opening of the orifice (valve V 2 position) remains same throughout the operation, equation (2) can be simplified as: Q o = C H (4) Where, C is a constant. So from equation (1) we can write that, Q C H = A dh (5) i dt The nonlinear nature of the process dynamics is evident from eqn.(5), due to the presence of the term H. In order to linearise the model and obtain a transfer function between the input and output, let us assume that initially Q i =Q o =Q s ; and the liquid level has attained a steady state value H s. Q Q C (H H ) = A dh i s 2 H s s dt d(h (7)
Now, we define the variables q and h, as the deviations from the steady state values, q = Q i Q s (8) h = H H s We can write from (7), q = A dh + 1 h (9) dt R H s Where, R = 2 (10) C It can be easily seen, that eqn.(9) is a linear differential equation. So the transfer function of the process can easily be obtained as: h ( s ) R = (11) q ( s ) τ s + 1 Where, τ = RA. It is to be noted that all the input and output variables in the transfer function model represent, the deviations from the steady state values. If the operating point (the steady state level H s in the present case) changes, the parameters of the process (R andτ ) will also change. The importance of linearisation needs to be emphasized at this juncture. The mathematical models of most of the physical processes are nonlinear in nature; but most of the tools for design and analysis are for linear systems only. As a result, it is easier to design and evaluate the performance of a system if its mathematical model is available in linear form. Linearised model is an approximation of the actual model of the system, but it is preferred in order to have a physical insight of the system behaviour. It is to be kept in mind that this model is valid as long as the variation of the variables around the operating point is small. There are few systems whose dynamic behaviour is highly nonlinear and it is almost impossible to have a linear model of a system. For example, it is possible to develop the linearised transfer function model of an a.c. servomotor, but it is not possible for a step motor. Referring to Fig. 2, if the valve V 1 is motorized and operated by electrical signal, we can also develop the model relating the electrical input signal and the output. Again, we have so far assumed that the opening of the valve V 2 to be constant, during the operation. But if we also consider its variation, that would also affect the dynamics of the tank model. So, the effect of disturbance can be incorporated in the overall plant model, as shown in Fig.3, by introducing a disturbance transfer function D(s). D(s) can be easily by using the same methodology as described earlier in this section.
Process Degree of Freedom The state of a process or the configuration of a system is determined when each of its degrees of freedom is specified. Consider, for example, a ball placed on a billiard table. In order to specify its position, we would require three coordinates : One north-south coordinate, one east-west coordinate, and the height. However, the height is not arbitary because it is given by the height of the table surface above a reference plane. Consequently the ball has two degrees of freedom. Mathematically, the number of degrees of freedom is defined as n = nv ne (1.1) where n = number of degrees of freedom of a system nv = number of variables that describe the system ne = number of defining equations of the system or number of independent relationships that exist among the various variables. In the example of the billiard ball there are three variables of position (nv = 3), one defining equation (ne =1), and therefore two degrees of freedom (n = nu ne = 3 1 = 2). It is easy to see intuitively that a train has only one degree of freedom because only its speed can be varied, while boats have two and air planes have three When looking at industrial processes, the determination of degrees of freedom becomes more complex and cannot always be determined intuitively. The degrees of freedom of a process represents the maximum number of independently acting controllers that can be placed on that process. In other words, 'the number of independently acting automatic controllers on a system or process may not exceed the number of degrees of freedom.' System variables and parameters must be carefully distinguished. The weight of water in a tank, specific heat of water etc are parameters not variables. The inlet temperature, outlet temperature, water flow rate, heat input rate etc are variables. SERVO AND REGULATOR OPERATION Servomechanisms and Regulators are used to control the process either via automatic controllers or as a self contained unit. They are physically doing the job of adjusting the manipulated variable to have the controlled variable at around set point. A controller automatically adjusts one of the inputs to the process in response to a signal fed back from the process output. Servo Operation If the purpose of the control system is to make the process follow changes in the set point as closely as possible, such an operation is called servo operation. Changes in load variables such as uncontrolled flows, temperature and pressure cause large errors than the set point changes (normally in batch processes). In such cases servo operation is necessary. Though the set point changes quite slowly and steadily, the errors from load changes may be as large as the errors caused by the change of set point. In such cases also servo operation may be considered. A type of control system in common use, which has a slightly different objective from process control is called Servomechanism. In this case the objective is to force some parameter to vary in a specific manner. This may be called a tracking control system or a following control system. Instead of regulating a variable value to a set point, the servomechanism forces the controlled variable value to follow variation of the reference value. This kind of automatic control is characterized mainly by a variable desired value, but a fixed load. Powersteering of automobiles, ship- sheering mechanism, robot arm movements etc are some of the examples.
Regulator Operation In many of the process control applications, the purpose of control system is to keep the output (controlled variable) almost constant in spite of changes in load. Mostly in continuous processes the set point remains constant for longer time. Such an operation is called Regulator Operation. The set point generated and the actual value from sensors are given to a controller. The controller compares both the signals, generates error signal which is utilized to generate a final signal as controller output. The controller output is finally utilized to physically change the values of manipulated variable to achieve stability. The above action is achieved with the help of final control elements. They are operatable either with electrical, pneumatic or with hydraulic signals. The system that serves good for servo operation will generally not be the best for regulator operation. Large capacity or inertia helps to minimize error here whereas it makes the system sluggish in case of servo operation. If the setpoint changes quite slowly and steadily, but the error from the load changes is as large as if caused by sudden change of setpoint, the responses of both regulator and servo operations may be considered for such systems. SELF REGULATION A significant characteristic of some processes is the tendency to adopt a specific value of the controlled variable for nominal load with no control operations. Such a property of the process is called self-regulation. Consider the behaviour of the variable x shown in Fig. 1.46. Notice that at time t = t0 the constant value of x is disturbed by some external factors, but that as time progresses the value of x returns to its initial value and stays there. If x is a process variable such as temperature, pressure, concentration, or flow rate, we say that the process is stable or self-regulating and needs no external intervention for its stabilization. It is clear that no control mechanism is needed to force x to return to its initial value.