Control loop, dynamic elements

The dynamics of the process are usually very fast. The sensor sees the change in flow almost immediately. The control valve dynamics are the slowest element in the loop. So a small reset time can be used. 

It is important to remember that a deadtime or several lags must be inserted in most control loops in order to mn a relay-feedback test. To have an ultimate gain, the process must have a phase angle that drops below —180°. Many of the models in Aspen Dynamics have only a first-order transfer function between the controller variable and the manipulated variable. In the CSTR temperature controller example, the controlled variable is reactor temperature and the manipulated variable is medium temperature. The phase angle of a first-order process goes to only —90°, so there is no ultimate gain. The relay-feedback test will fail without the deadtime element inserted in the loop. 

For noninteracting control loops with zero dead time, the integral setting (minutes per repeat) is about 50% and the derivative, about 18% of the period of oscillation (P). As dead time rises, these percentages drop. If the dead time reaches 50% of the time constant, I = 40%, D = 16%, and if dead time equals the time constant, I = 33% and D = 13%. When tuning the feedforward control loops, one has to separately consider the steady-state portion of the heat transfer process (flow times temperature difference) and its dynamic compensation. The dynamic compensation of the steady-state model by a lead/lag element is necessary, because the response is not instantaneous but affected by both the dead time and the time constant of the process. 

The key to effective troubleshooting is expressed in the old adage, divide and conquer. It is important to locate the portion of the control loop hardware that is causing the poor performance the hnal control element, the sensor system, the controller, or the process. The place to start is to test each system separately to determine whether that portion of the control loop is operating properly. The hnal control element can be evalnated by applying a series of input step tests. That is, the input to the hnal control element, which is normally set by the controller, can be manually adjusted. The test allows the determination of the dynamic response and deadband of the actuator system. If the performance in these two areas is satisfactory, there is no need to evaluate the actuator system further. 

In the feedback control loop of Figure 29.9 we have omitted the dynamics of the measuring sensor and final control element. Thus they are absent from the closed-loop response of eq. (29.21). Consider the loop of Figure 29.10, with the sensor and final control element included. Following the same procedure as above, it is easy to show that the sampled-value, closed-loop response of the loop is given by... 

Consider the block diagram of a direct digital feedback control loop shown in Figure 29.9. Such loops contain both continuous- and discrete-time signals and dynamic elements. Three samplers are present to indicate the discrete-time nature of the set point j/Sp( ), control command c(z), and sampled process output y(z). The continuous signals are denoted by their Laplace transforms [i.e., y(s), Jn(s), and d(s)]. Furthermore, the continuous dynamic elements (e.g., hold, process, disturbance element) are denoted by their continuous transfer functions, H(s), Gp(s), and GAs), respectively. For the control algorithm, which is the only discrete element, we have used its discrete transfer function, D(z). 

The design and use of a servomechanism control system requires a knowledge of every element of the control loop. For example, in Figure 1 the engineer must know the dynamic response, or complete operating characteristics, of each pictured device ... 

While this approach results in a significant improvement in computation time, the approximate solution may not be accurate enough for the application. Particularly, where control applications are concerned, these unstructured elements are related to the integral part of the control loops and an inaccurate solution may have catastrophic effects mainly if the process is highly dynamic (e.g., surge lines and radicalic systems), where the correction selection of the discretization time of the control action is also critical. 

In the first place the degree of automation has to be fixed. Very simple manually operated experimental plants may only need few measuring and indicating instruments placed in the location of the measurement in question, hand-operated controllers and final control elements. With an increasing number of control loops and registers the burden on the personnel decreases. The control system characteristics have to be adapted to the dynamic behaviour of the control loop. Controllers with the following characteristics are distinguished (cf. [1]) ... 

Installing temperature and composition controllers is somewhat more involved than installing level and flow controllers because of three issues. First, we need to include additional dynamic elements in the loop. Temperature and composition measurements... 

Fortunately, a process need not be very complicated before the properties of the typical feedback loop make their appearance. A rapid introduction to loop behavior may be presented using the simplest dynamic element found in the process-dead time. This chapter is devoted exclusively to discussion of the control of simple dynamic ele-... 

It has already been pointed out that negative feedback, being negative, introduces 180 of phase shift. This means that if a closed loop is to oscillate, the dynamic elements in the controller and the process must contribute an additional 180 . 

The natural period of any loop depends on the combination of all dynamic elements within it, including the controller. Since the amount of phase lag of most dynamic elements varies with the period of the wave passing through them, there is one particular period at which the total phase lag will equal 180 . This is the period at which the loop naturally resonates. The natural period is a dependent variable. We can make use of its relation to the process dynamics in two ways ... 

Dynamic Elements in the Control Loop TABLE 1. 1 Settings of Proportional and Reset for 3 -amplitude Damping... 

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