Classical feedback control

If T(s) = 1 and S(s) = 0 there is perfeet set-point traeking and disturbanee rejeetion. This requires that G(s)C(s) is strietly proper (has more poles than zeros), so that 

if T(s) = 1, there will be both perfeet set-point traeking and noise aeeeptanee. Considering the problem in the frequeney domain however, it may be possible that at low frequeneies T ]uj) 1 (good set-point traeking) and at high frequeneies T ]uj) 0 (good noise rejeetion). 

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Classical Feedback Control. The majority of controllers ia a continuous process plant is of the linear feedback controller type. These controllers utilize one or more of three basic modes of control proportional (P), iategral (I), and derivative (D) action (1,2,6,7). In the days of pneumatic or electrical analogue controllers, these modes were implemented ia the controller by hardware devices. These controllers implemented all or parts of the foUowiag control algorithm ... 

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... 

Figure 9.18 shows a classical feedback control system D s) is a disturbance input, N s) is measurement noise, and therefore... 

We use a simple liquid level controller to illustrate the concept of a classic feedback control system.1 In this example (Fig. 5.1), we monitor the liquid level in a vessel and use the information to adjust the opening of an effluent valve to keep the liquid level at some user-specified value (the set point or reference). In this case, the liquid level is both the measured variable and the controlled variable—they are the same in a single-input single-output (SISO) system. In this respect, the controlled variable is also the output variable of the SISO system. A system refers to the process which we need to control plus the controller and accompanying accessories such as sensors and actuators.2... 

In the preceding section we identified the critical need for more effective control of processes with significant dead time. In this section we discuss a modification of the classical feedback control system which was proposed by O. J. M. Smith for the compensation of dead-time effects. It is known as the Smith predictor or the dead-time compensator. 

Fig. 18. Dead-time compensation (a) classical feedback and (b) Smith dead-time compensator. SP = setpoint C = controlled variable and (+) and (—)...

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. 

We now return to the use of state space representation that was introduced in Chapter 4. As you may have guessed, we want to design control systems based on state space analysis. State feedback controller is very different from the classical PID controller. Our treatment remains introductory, and we will stay with linear or linearized SISO systems. Nevertheless, the topics here should enlighten( ) us as to what modem control is all about. 

The state feedback gain including integral control K is [0 1.66 -4.99], Unlike the simple proportional gain, we cannot expect that Kn+1 = 4.99 would resemble the integral time constant in classical PI control. To do the time domain simulation, the task is similar to the hints that we provide for Example 7.5B in the Review Problems. The actual statements will also be provided on our Web Support. 

Apply classical controller analysis to cascade control, feedforward control, feedforward-feedback control, ratio control, and the Smith predictor for time delay compensation. 

The ar tide is organized as follows. We will begin with a discussion of the various possibilities of dynamical description, clarify what is meant by nonlinear quantum dynamics , discuss its connection to nonlinear classical dynamics, and then study two experimentally relevant examples of quantum nonlinearity - (i) the existence of chaos in quantum dynamical systems far from the classical regime, and (ii) real-time quantum feedback control. 

To illustrate an application of nonlinear quantum dynamics, we now consider real-time control of quantum dynamical systems. Feedback control is essential for the operation of complex engineered systems, such as aircraft and industrial plants. As active manipulation and engineering of quantum systems becomes routine, quantum feedback control is expected to play a key role in applications such as precision measurement and quantum information processing. The primary difference between the quantum and classical situations, aside from dynamical differences, is the active nature of quantum measurements. As an example, in classical theory the more information one extracts from a system, the better one is potentially able to control it, but, due to backaction, this no longer holds true quantum mechanically. 

The more classical Itinehoii of parathyroid hormone is concerned with its control of the maintenance of constant circulating calcium levels. Its action is on 11) Ihe kidney, where it increases the phosphate in the urine. (2) the skeletal system, where it causes calcium resorplion from bone, and t3l the digestive system, where it accelerates (stimulates) calcium absorption into the hitskI The hormone and gland exhibit characteristics of feedback control when the concentration of calcium tons in the blood falls, the secretion of the hormone increases, and when their concentration rises, the secretion of hormone decreases... 

Discrete time controllers will not normally be stand-alone units but will be simulated within the software of a digital computer. The capacity of the computer can be used if necessary to produce more complex forms of feedback control than those provided by the standard algorithms of the classical fixed parameter controller. 

Cortisol also plays a role in controlling the release of CRH and ACTH from the hypothalamus and pituitary, respectively. As illustrated in Figure 29-2, the relationship between plasma cortisol and CRH and ACTH release is a classic example of a negative feedback control system. Increased plasma cortisol levels serve to inhibit subsequent release of CRH and ACTH, thus helping to maintain homeostasis by moderating glucocorticoid activity. 

The control of ribonucleotide reductase activity is affected in the classic feedback fashion by cellular nucleotide concentrations. dATP inhibits the reduction of all four ribonucleoside diphosphates. dTTP inhibits the reduction of only CDP and UDP. ATP is the positive effector for the reduction of these two nucleotides, and both dTTP and dGTP stimulate the reduction of GDP and ADP. Hydroxyurea, an antitumor agent, inhibits ribonucleotide reductase, and this depletes the deoxyribonucleotide supply required for tumor DNA biosynthesis. 

Although the mechanisms for the control of cell division in tissues are largely unknown, it is clear in normal situations that cells divide only if new cells are needed. A classic example is the liver, which can regenerates its normal mass within a week or so after removal of two-thirds of its mass. Other tissues exhibit a smaller type of limited cell division. Whatever the normal feedback control mechanisms, it is clear that cancer cells have lost the normal growth controls and continue to divide in an uncontrolled manner until the host is destroyed. 

The use of PID controllers should be restricted to those loops where two criteria are both satisfied the controlled variable should have a very large signal-to-noise ratio and tight dynamic control is really essential from a feedback control stability perspective. The classical example of the latter is temperature control in an irreversible exothermic chemical reactor (see Chap. 4). 

Therefore, the controller is a linear time-invariant controller, and no online optimization is needed. Linear control theory, for which there is a vast literature, can equivalently be used in the analysis or design of unconstrained MPC (Garcia and Morari, 1982). A similar result can be obtained for several MPC variants, as long as the objective function in Eq. (4). remains a quadratic function of Uoptfe+ -iife and the process model in Eq. (22) remains linear in Uoptfe+f-ife. Incidentally, notice that the appearance of the measured process output y[ ] in Eq. (22) introduces the measurement information needed for MPC to be a feedback controller. This is in the spirit of classical hnear optimal control theory, in which the controlled... 

A common performance estimation method in classical single-loop feedback controller design is to check the open-loop disturbance rejection of a system up to the point in time at which the controller action is assumed to take effect. If constraints are violated during this time, the controller cannot prevent the violation. The use of this test can be traced back to Velguth and Anderson (1954). 

The IMC structure, illustrated in Figure 21.22a, includes the process, p s), the process model, p i, and the IMC controller, s. This structure is equivalent to the classic feedback structure, shown in Figure 21.22b, in which c s is the feedback controller. It is convenient to carry out design using the IMC structure, and then implement the control system using the classic feedback structure, with c s computed using the equation... 

ABSTRACT Smart structures usually incorporate some control schemes that allow them to react against disturbances. In mechanics we have in mind suppression of mechanical vibrations with possible applications on noise and vibration isolation. A model problem of a smart beam with embedded piezoelectric sensors and actuators is used in this paper. Vibration suppression is realized by using active control. Classical mathematical control usually gives good results for linear feedback laws under given assumptions. The design of nonlinear controllers based on fuzzy inference rules is proposed and tested in this chapter. 

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