Elements, control loops

The controller function will take on a positive pole if the process function has a positive zero. It is not desirable to have an inherently unstable element in our control loop. This is an issue which internal model control will address. 

So far, we know that the secondary loop helps to reduce disturbance in the manipulated variable. If we design the control loop properly, we should also accomplish a faster response in the actuating element the regulating valve. To go one step further, cascade control can even help to make the entire system more stable. These points may not be intuitive. We ll use a simple example to illustrate these features. 

B) in Figure 9 represents the lube oil temperature control loop in block diagram form. The lube oil cooler is the plant in this example, and its controlled output is the lube oil temperature. The temperature transmitter is the feedback element. It senses the controlled output and lube oil temperature and produces the feedback signal. 

The actuating signal passes through the two control elements the temperature controller and the temperature control valve. The temperature control valve responds by adjusting the manipulated variable (the cooling water flow rate). The lube oil temperature changes in response to the different water flow rate, and the control loop is complete. 

Controllers are the controlling element of a control loop. Their function is to maintain a process variable (pressure, temperature, level, etc.) at some desired value. This value may or may not be constant. 

The sensor element constitutes a palladium-nickel alloy resistor with a temperature sensor and a proprietary coating. The sensor has a broad operating temperature range and a sophisticated temperature control loop that includes a heater and a temperature sensor, which controls the die temperature within 0.1°C. 

The measuring and final control elements in the control loop are described by transfer functions which can be approximated by constants of unit gain, and the process has the transfer function ... 

Determine the open-loop response of the output of the measuring element in Problem 7.17 to a unit step change in input to the process. Hence determine the controller settings for the control loop by the Cohen-Coon and ITAE methods for P, PI and PID control actions. Compare the settings obtained with those in Problem 7.17. 

A unity feedback control loop consists of a non-linear element N and a number of linear elements in series which together approximate to the transfer function ... 

Real-life operational practice will not always correspond neatly with the theoretical control model derived in the previous Chapter, which is characterized by a completely closed control loop. Never-the-less, to better understand any malfunction of an operational process, it is worthwhile to map that process on the theoretical control model and to identify the ineffective control elements (observation, judgement, intervention, steering) in practice. By identifying ineffective control elements, one will get a clear picture why precursors exist. In this sub-Section the different control models and their ineffective elements are identified. 

In the double loop scheme of Figure 35 (right in Figure 35) the effectiveness of the steering process is checked in addition, in case of any ineffective control elements. To do so, an additional condition is tested, i.e. the norm provided by the steering element (double loop) is questioned. Only if one or both of the following criteria is satisfied, then the steering process is considered to be ineffective ... 

In the next steps the elements of the single control loop, i.e. the control elements observation , judgement and intervention , are checked by questioning their presence and effectiveness, according to the left flow scheme of Figure 35 (single loop). 

In case of any ineffective control elements the double control loop is checked by questioning the presence and effectiveness of the corresponding norm. This is illustrated by the right flow scheme of Figure 35 (double loop). 

The uncertainty in the identified number of ineffective elements, indicated by the unknown class, grows with the position of the element in the control loop, e.g. the uncertainty about the number of ineffective interventions is larger than the uncertainty about the number of ineffective judgements. 

Including the double-loop of the control loop, it can be concluded that for at least 60% of the ineffective control elements, the origin of the ineffectiveness has to be sought in the steering element instead of in the ineffective control element itself. From this it is concluded that the steering element of the operational control level (which are the higher control levels in an organization) is the main cause for ineffective control loops. 

We will consider all the components of this temperature control loop in more detail later in this book. For now we need only appreciate the fact that the automatic control of some variable in a process requires the installation of a sensor, a transmitter, a controller, and a final control element (usually a control valve). Most of this book is aimed at learning how to decide what type of controller should be used and how it should be tuned, i.e., how should the adjustable tuning parameters in the controller be set so that we do a good job of controlling temperature. 

The interface with the process at the other end of the control loop is made by the final control element. In a vast majority of chemical engineering processes the final control element is an automatic control valve which throttles the flow of a manipulated variable. Most control valves consist of a plug on the end of a stem that opens or closes an orifice opening as the stem is raised or lowered. As sketched in Fig. 7.5, the stem is attached to a diaphragm that is driven by changing air pressure above the diaphragm. The force of the air pressure is opposed by a spring. 

In the previous chapter we discussed the elements of a conventional single-input-single-output (SISO) feedback control loop. This configuration forms the backbone of almost all process control structures. 

The behaviour of many control loop components can be described by first-order differential equations provided that certain simplifying assumptions are made. Great care should be taken that the assumptions made are reasonable under the conditions to which the component is subjected. Two examples of a first-order system are described—a measuring element and a process. An illustration of a multivariable system which approximates to first order with respect to each input variable can be found in Example 7.11. 

Once each element in any feedback control loop has been described in terms of its transfer function, the behaviour of the closed-loop can be determined by the formulation of appropriate closed-loop transfer functions. Two such are of importance, i.e. those relating the controlled variable C to the set point R and to the load U, respectively. 

Consider the control loop shown in Fig. 7.44. Suppose the loop to be broken after the measuring element, and that a sinusoidal forcing function M sin cot is applied to the set point R. Suppose also that the open-loop gain (or amplitude ratio) of the system is unity and that the phase shift xj/ is -180°. Then the output JB from the measuring element (i.e. the system open-loop response) will have the form ... 

The presence of significant amounts of dead time in a control loop can cause severe degradation of the control action due to the additional phase lag that it contributes (see Example 7.7). One method for compensating for the effects of dead time in the control loop has been suggested by SMITH<30>. This consists of the insertion of an additional element which is often termed the Smith predictor as it attempts to predict the delayed effect that the manipulated variable will have upon the process output. 

The analysis of the stability of a control system which contains a non-linear element that can be characterised by a describing function N is facilitated by considering the non-linear element as a variable gain for which N depends upon the amplitude M of the input signal(40). The behaviour (in terms of frequency response) of linear elements in the control loop will be a function of frequency only. 

Fig. 7.92. Control loop containing a sampler and a zero-order hold element (a) block diagram (b) output of hold element (filter)...

H, H, Transfer function of measuring element or of elements in feedback path of control loop ... 

---