Feedback loop control

Feedback control systems can be either analogue, where the controller is a mechanical device, or digital, where the controller is a computer or 

How often the control loop is executed is determined by the sampling interval, which is how often the measurement is taken. A critical pressure on an exothermic reactor may be sampled several times per second, while the level of a buffer tank may only be sampled a few times an hour. The sampling time must be chosen with care to ensure that possible changes in the process are detected early enough for the controller to take appropriate action. However, sampling too often is undesirable as it may upset the process and because a large number of data points would have to be sampled and stored. 

The most commonly used controller in the process industries is the three term or PID controller. This controller is a feedback controller and adjusts the manipulated variable in proportion to the change in its output signal, c, from its steady state value (bias), cs, on the basis of a measurement of the error in the controlled variable, s, which is given by 

The relationship involves three terms and three adjustable parameters, the controller gain, Kc, the integral time, xl3 and the derivative time, Td (hence the name). Finding the right values of these parameters for the best possible control action is called tuning. There are several techniques available for controller tuning as will be discussed later. 

1 Proportional Action. Control action is proportional to the size of the error, and Equation 2 becomes  

Both steady-state and dynamic response characteristics affect loop performance. Steady-state gain is the most basic and important of these response characteristics. Gain for a block element can be simply defined as the ratio of change in output to a change in input. For several blocks in series, the resulting overall gain is the product of the individual block gains. 

Dynamic responses can be divided into the categories of selfregulating and non-self-regulating. A self-regulating response has inherent negative feedback and will always reach a new steady-state in response to an input change. Self-regulating response dynamics can be approximated with a combination of a deadtime and a first-order lag with an appropriate time constant. 

A run-away response continues to change at an increasing rate due to inherent positive feedback. The response is exponential and may be thought of as a first-order lag with a negative time constant. Run-away response dynamics may be approximated with a combination of deadtime, a first-order lag, and a second, longer lag with a negative time constant. 

One common nonlinear characteristic of control valves is hysteresis, which results in two possible flows at a given valve position, depending on whether the valve is opening or closing. In the steady-state, hysteresis limits resolution in achieving a specific flow with its desired effect on the process. Dynamically, hysteresis also creates pre-stoke deadtime, which contributes to total loop deadtime, thus degrading the performance of the loop. Pre-stroke deadtime is the time that elapses as the controller output slowly traverses across 

The use of a valve positioner can significantly reduce both hysteresis and pre-stroke deadtime. A valve positioner is recommended for all control loops requiring good performance. Typical hysteresis may be 2-5% for a valve without a positioner, 0.5-2% for a valve with an analog positioner, and 0.2-0.5% for a valve with a digital positioner. 

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Dead-Time Compensation. Dead time within a control loop can greatiy iacrease the difficulty of close control usiag a PID controller. Consider a classical feedback control loop (Fig. 18a) where the process has a dead time of If the setpoiat is suddenly iacreased at time t, the controller immediately senses the deviation and adjusts its output. However, because of the dead time ia the loop, the coatroUer does aot begia to see the impact of that change ia its feedback sigaal, that is, a reductioa ia the deviatioa from setpoiat, uatil the time t +. Because the deviatioa does aot change uatil... 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

A control system may have several feedback control loops. For example, with a ship autopilot, the rudder-angle control loop is termed the minor loop, whereas the heading control loop is referred to as the major loop. When analysing multiple loop systems, the minor loops are considered first, until the system is reduced to a single overall closed-loop transfer function. 

The components of the basic feedback control loop, combining the process and the controller can be best understood using a generalised block diagram (Fig. 2.29). The information on the measured variable, temperature, taken from the system is used to manipulate the flow rate of the cooling water in order to keep the temperature at the desired constant value, or setpoint. This is illustrated by the simulation example TEMPCONT, Sec. 5.7.1. 

Addition of a feedback control loop can stabilize or destabilize a process. We will see plenty examples of the latter. For now, we use the classic example of trying to stabilize an open-loop unstable process. 

In Eq. (10-5), 1/Gp is the set point tracking controller. This is what we need if we install only a feedforward controller, which in reality, we seldom do.4 Under most circumstances, the change in set point is handled by a feedback control loop, and we only need to implement the second term of (10-5). The transfer function -GL/Gp is the feedforward controller (or the disturbance rejection... 

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 ... 

Devise a feedback control loop to correct for any imperfections in the feedforward controller. 

One of the most important items to check in setting up a feedback control loop on the plant is that the action of the controller is correct. 

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. 

As was pointed out, the most important drawback in the operation of AD processes is related to the instability of the process. However, this drawback can be overcome by associating monitoring procedures with decision support systems that allow the on-line stable operation of the process via a feedback control loop [27, 33]. Nowadays, most of the monitoring and control techniques available in the literature belong to those called model-based . Such... 

Does not have a Sensor-Feedback Control Loop. Digital Setpoint Only. 

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. 

Fig. 7.37 Simple feedback control loop with feedback path represented by a steady-state...

An inherently stable process can be destabilised by the addition of a feedback control loop—particularly where integral action is included. This is illustrated in the following example using the characteristic equation and the Routh-Hurwitz stability criterion. 

A negative phase margin indicates an unstable system. Clearly, first and second order systems are inherently stable as the maximum phase shift of the former is -90° and of the latter -180° (Section 7.8.4). (Note that when such a system is included within a feedback control loop this innate stability may no longer exist—see Section 7.10.3.)... 

In the following example the effect of the various fixed parameter control modes on the stability of a simple feedback control loop are examined using the Bode stability criterion and the concept of gain and phase margins. 

Fig. 7.59. Simple feedback control loop with significant dead time in the process...

Imperfections in feed-forward control can often be overcome by the addition of suitable feedback action. A typical design is shown in Fig. 7.70 where any variations in xd which occur bring the feedback control loop into action. The reflux flow is shown on flow control in cascade with the boiling temperature of the liquid at an appropriate point within the column. The inner (or slave) flow controller maintains... 

The feedback control loop consists in measuring the height, comparing it with the set point, i.e., the height for the input flow rate of 2.3 to3/hour, and using the... 

To keep the plant at its middle unstable steady state can be achieved by stabilizing the unstable steady state with a simple feedback control loop. For the sake of simplicity, we use a SISO (single input single output) proportional feedback control, in which the dense-phase temperature of the reactor is the controlled measured variable, while the manipulated variable can be any of the input variables of the system Yfa, FCD, etc. We use Yfa as the manipulated variable here. The set-point of the proportional controller is the dense-phase reactor temperature at the desired middle steady state in this case. Our simple SISO control law is... 

Its function is to expand the pressurized solution to separate the "solvent gas" from dissolved extracted components. If a fixed restrictor is used, the mass flow rate of the fluid changes as a function of pressure (density) mass flow can increase by a factor of 25 as pressure is increased from 80 to 400 bar (24). Not only are the pressure and flow coupled, the coupling is via a static conduit whose dimensions are imprecisely controlled during an extraction (partial plugging by particulates and precipitated components, temperature) and from component to component during maintenance replacements. This results in a lack of control in operating parameters (density) and timed sequences (via flow rate and time). A variable restrictor whose dimensions are set and adjusted by an electronic feedback control loop is an alternative solution. 

A feedback control loop is generally illustrated as shown in Figure 6. The Process refers to the chemical or physical process (the tank in the example earlier). The Measuring Device is used to measure the value of the variable that is to be controlled (the level indicator in the tank example or a thermometer in a shower). The Control Element (usually a flow control valve or the setting on a heater or cooler) changes the value of the manipulated variable. The manipulated variable is the variable used to change the controlled variable (in the tank example, the output flow rate is the manipulated variable used to change the level in the tank, which is the controlled variable). 

Shinsky (1979) uses a relative gain matrix to select which variables to manipulate and measure. Again dynamics are ignored. The method allows one to find which variables influence which others the most if they were put into a feedback control loop. 

We say that the inventory is self-regulating. Similarly, the plantwide control can fix the flow rate of reactant at the plant inlet. When the reactant accumulates, the consumption rate increases until it balances the feed rate. This strategy is based on a self-regulation property. The second strategy is based on feedback control of the inventory. This consists of measuring the component inventory and implementing a feedback control loop, as in Fig. 4.2(b). Thus, the increase or decrease of the reactant inventory is compensated by less or more reactant being added into the process. 

Once we identify the dominant variables, we must also identify the manipulators (control valves) that are most suitable to control them. The manipulators are used in feedback control loops to hold the dominant variables at setpoint. The setpoints are then adjusted to achieve the desired production rate, in addition to satisfying other economic control objectives. 

A few comments about the method are warranted. The controlled (dominant) variables, Ycd, should be measured such that they belong to the set Yd for rapid control. Similarly, the manipulators in the feedback control loops should belong to the set, Ud. The feedback controllers should have integral action (PI controllers). These can be tuned with minimal information (e.g., ultimate gain and frequency from a relay test). The model Ms is usually quite simple and can be developed from operating data using statistical regressions. This works because the model includes all the dominant variables of the system, Y d, as independent variables by way of their setpoints, Y. The definition of domi-... 

Shu (S6) has taken advantage of the dependence of fermentor performance on agitator speed, by setting up a feedback control loop in which the agitator speed is varied automatically so as to cause the broth oxygen uptake to vary with time in a predetermined manner. 

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