Closed-Loop System with Feedback

Suppose the objective is to control the temperature of a bioreactor. The temperature of a bioreactor is measured by instrumentation and compared with a set-point value. Based on the difference between the measured and the set-point temperature, the flow rate of cooling water into a fermentor jacket is increased or decreased by manipulating a control valve of cooling water until the difference between the measured and the set-point temperature becomes zero. By repeating this operation, the temperature of a bioreactor can be kept constant regardless of changes in the outer temperature or from the internal generation of heat. 

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A closed-loop system with feedback, which is illustrated in Figure 13.2, is the central feature of a control system in bioprocess control, as well as in other processing industries. First, a set-point is established for a process variable. Then, the process variable measured in a bioreactor is compared with the set-point value to determine a deviation e. Based on the deviation, a controller uses an algorithm to calculate an output signal O that determines a control action to manipulate a control variable. By repeating this cycle during operation, successful process control is performed. The controller can be the operator when manual control is being employed. 

Figure 9.1. Closed-loop system with state feedback...

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

Figure 20. Simulated conversion response of continuous polymerization system to a load disturbance under closed-loop control with IAE optimum controller tuning constants and manipulation of initiator flow rate at 0.06 mol/L H20 surfactant and 50°C catalyst feed concentration—STD feedback (-) vs.

Both u(x) and Jopt(x) are discontinuous at the origin. Therefore, stability theorems that rely on continuity cannot be used. Yet, it is simple to check by inspection that the feedback law of Eq. (71) (with either sign chosen) is asymptotically stabilizing. However, the continuous feedback control law u(x) = 0, resulting in the closed-loop system... 

Yuzhakov et al. [93] describe the production of an intracutaneous microneedle array and provide an account of its use (microfabrication technology). Various embodiments of this invention can include a microneedle array as part of a closed loop system smart patch to control drug delivery based on feedback information from analysis of body fluids. Dual purpose hollow microneedle systems for transdermal delivery and extraction which can be coupled with electrotransport methods are also described by Trautman et al. [91] and Allen et al. [100]. These mechanical microdevices which interface with electronics in order to achieve a programmed or controlled drug release are referred to as microelectromechanical systems (MEMS) devices. 

It is interesting to note that there is increased secretion of corticoid after trauma in the face of elevated plasma levels. Some confusion over the mechanisms controlling plasma corticoid has arisen because of this, and two control mechanisms have been proposed, a closed-loop control with negative feedback, in nonstress conditions and an open-loop control with no feedback, in stress. However, Yates and Urquhart (Yl) point out the most likely control system is a closed-loop, negative feedback proportional control, with a variable set point, the set point being raised in stress. Why the set point should be raised (or the type of control changed) in stress when all the evidence indicates a noncausal role for corticoid in the various other responses to stress is a very interesting and as yet unanswered question. 

Figure 18.7 shows that curve A does not encircle the point (-1,0), whereas curve B does. Thus, according to the Nyquist criterion, the feedback system with open-loop Nyquist plot the curve A is stable, while curve B indicates an unstable closed-loop system. This in turn implies that for Kc = 1 the system is stable, whereas for Kc = 50 it is unstable. 

While designing a feedback control system (i.e., selecting its components and tuning its controller), we are seriously concerned about its stability characteristics. Therefore, before we proceed with the particular details of designing a feedback control loop, we will study the notion of stability and analyze the stability characteristics of closed-loop systems. 

The sensors produce signals with contributions from neglected structural modes. If this t3rpe, known as observation spillover, coincides with control spillover in the case of observer-based state feedback control, destabilization of the closed-loop system may be the consequence. 

With this continuous real-time data stream on the polymer properties and reaction kinetics, it is anticipated that ACOMP will allow for immediate benefits with tighter operator control. Evenmally, the goal will be to use the continuous stream of process data on polymer properties and reaction kinetics yielded by ACOMP to create a complete feedback control closed loop system. This will be achieved by developing low-error process control models using ACOMP and general process data. This union of ACOMP with process models... 

An important consequence of feedback control is that it can cause oscillatory responses. If the oscillation has a small amplitude and damps out quickly, then the control system performance is generally considered to be satisfactory. However, under certain circumstances, the oscillations may be undamped or even have an amplitude that increases with time until a physical limit is reached, such as a control valve being fully open or completely shut. In these situations, the closed-loop system is said to be unstable. 

Having dealt with the stability of closed-loop systems, we can consider our next topic, the design of feedback control systems. This important subject is considered in Chapters 12 and 14. A number of prominent control system design and tuning techniques are based on stability criteria. 

In this section we present an advanced control technique, time-delay compensation, which deals with a problematic area in process control—namely, the occurrence of significant time delays. Time delays commonly occur in the process industries because of the presence of distance velocity lags, recycle loops, and the analysis time associated with composition measurement. As discussed in Chapters 12 and 14, the presence of time delays in a process hmits the performance of a conventional feedback control system. From a frequency response perspective, a time delay adds phase lag to the feedback loop, which adversely affects closed-loop stabihty. Consequently, the controller gain must be reduced below the value that could be used if no time delay were present, and the response of the closed-loop system will be sluggish compared to that of the control loop with no time delay. 

With this technology it is now possible to achieve extremely accurate speed control of the order of 0.01 % to 0.001 %. To achieve such high accuracy in speed control, closed-loop feedback control systems and microprocessor-based control logistics can be introduced into the inverter control scheme to sense, monitor and control the variable parameters of the motor to very precise limits. 

Any system in which the output quantity is monitored and compared with the input, any difference being used to actuate the system until the output equals the input is called a closed-loop or feedback control system. 

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. 

Fig. 8.10 Closed-loop control system with full-order observer state feedback.

Example 2.15. Derive the closed-loop transfer function C/R for the system with three overlapping negative feedback loops in Fig. E2.15(a). 

In our examples, we will take Gm = Ga = 1, and use a servo system with L = 0 to highlight the basic ideas. The algebra tends to be more tractable in this simplified unity feedback system with only Gc and Gp (Fig. 5.6), and the closed-loop transfer function is... 

The state space state feedback gain (K2) related to the output variable C2 is the same as the proportional gain obtained with root locus. Given any set of closed-loop poles, we can find the state feedback gain of a controllable system using state-space pole placement methods. The use of root locus is not necessary, but it is a handy tool that we can take advantage of. 

To find the new state feedback gain is a matter of applying Eq. (9-29) and the Ackermann s formula. The hard part is to make an intelligent decision on the choice of closed-loop poles. Following the lead of Example 4.7B, we use root locus plots to help us. With the understanding that we have two open-loop poles at -4 and -5, a reasonable choice of the integral time constant is 1/3 min. With the open-loop zero at -3, the reactor system is always stable, and the dominant closed-loop pole is real and the reactor system will not suffer from excessive oscillation. 

Feedback is information in a closed-loop control system about the condition of a process variable. This variable is compared with a desired condition to produce the proper control action on the process. Information is continually "fed back" to the control circuit in response to control action. In the previous example, the actual storage tank water level, sensed by the level transmitter, is feedback to the level controller. This feedback is compared with a desired level to produce the required control action that will position the level control as needed to maintain the desired level. Figure 3 shows this relationship. 

The simulations involve the solution of the rigorous tray-by-tray model of each sequence, given by equations 1 to 6, together with the standard equations for the PI controllers for each control loop (with the parameters obtained through the minimization of the lAE criterion). The objective of the simulations is to And out how the dynamic behavior of the systems compare under feedback control mode. To carry out the closed-loop analysis, two types of cases were considered i) servo control, in which a step change was induced in the set point for each product composition under SISO feedback control. 

Thus we have described a system and process having a multiplicity of iterative feedbacks and feedforwards from each component and subprocess, to every other component and subprocess, all increasing the energy collected in the system and furnished to the load. In open-loop operation, this results in COP >1.0 permissibly, since the excess energy is freely received from an external source. In closed-loop operation, the COP concept does not apply except with respect to operational efficiency. In that case, the operational... 

The notion of quantum feedback control naturally suggests a closed-loop process in the laboratory to stabilize or guide a system to a desired state. In addition, feedback is important in the design of molecular controls. These points will be made clear below, starting with considerations of design followed by a discussion of its role in the laboratory and finally leading to feedback concepts for the inversion of laboratory data. 

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