Control systems with multiple loops

Block diagram reduction Control systems with multiple loops 

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. 

To reduce complexity, in the following examples the function of. v notation (.v) used for transfer functions is only included in the final solution. 

Now Gmi is multiplied by, or in cascade with G2. Hence the combined transfer function is 

Following a similar process, the second minor loop Gmi may be written 

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In such cases control systems with multiple loops may arise. Typical examples of such configurations, that we will study in the present chapter, are the following ... 

Chap. 20 Control Systems with Multiple Loops... 

Recognize that these ranges are approximate and that it may not be possible to choose PI or PID controller settings that result in specified GM and PM values. Tan et al. (1999) have developed graphical procedures for designing PI and PID controllers that satisfy GM and PM specifications. The GM and PM concepts are easily evaluated when the open-loop system does not have multiple values of 0) or Wg. However, for systems with multiple o)g, gain margins can be determined from Nyquist plots (Doyle et al., 1992). 

A major disadvantage of this system is the limitation of the single-pass gas-chlorination phase. Unless increased pressure is used, this equipment is unable to achieve higher concentrations of chlorine as an aid to a more complete and controllable reaction with the chlorite ion. The French have developed a variation of this process using a multiple-pass enrichment loop on the chlorinator to achieve a much higher concentration of chlorine and thereby quickly attain the optimum pH for maximum conversion to chlorine dioxide. By using a multiple-pass recirculation system, the chlorine solution concentrates to a level of 5-6 g/1. At this concentration, the pH of the solution reduces to 3.0 and thereby provides the low pH level necessary for efficient chlorine dioxide production. A single pass results in a chlorine concentration in water of about 1 g/1, which produces a pH of 4 to 5. If sodium chlorite solution is added at this pH, only about 60 percent yield of chlorine dioxide is achieved. The remainder is unreacted chlorine (in solution) and... 

We noted earlier in this chapter that many reactions in the chemical industries are exothermic and require heat removal. A simple way of meeting this objective is to design an adiabatic reactor. The reaction heat is then automatically exported with the hot exit stream. No control system is required, making this a preferred way of designing the process. However, adiabatic operation may not always be feasible. In plug-flow systems the exit temperature may be too hot due to a minimum inlet temperature and the adiabatic temperature rise. Systems with baekmixing suffer from other problems in that they face the awkward possibilities of multiplicity and open-loop instability. The net result is that we need external cooling on many industrial reactors. This also carries with it a control system to ensure that the correct amount of heat is removed at all times. 

A first control scheme proposed in [90] is shown in Fig. 10.26. In this scheme, product purities of methyl acetate (MeAC) and water (HjO) are inferred from temperatures on trays 3 and 12, respectively, and the feed rates of methanol (MeOH) and acetic acid (AcH) are used as manipulated variables. For this configuration, three different temperature profiles exist with identical temperature values at the sensor locations but different feed rates and completely different product compositions. The solid line in Fig. 10.26 represents the desired temperature profile with high conversion. This situation corresponds to input multiplicity as introduced at the beginning of section 10.2 on multiplicity and oscillations. Here, the same set of output variables (temperatures) is produced by (three) different sets of input variables (feed rates). Because the steady state values of the output variables are fixed by the given setpoint of the controllers, this input multiplicity will lead to steady state multiplicity of the closed loop system as illustrated in Fig. 10.27. 

External field-mediated assembly techniques offer flexible and robust control of micro components in fluidic systems. Simultaneous use of multiple fields helps eliminate the disadvantages of individual methods and enables more complex assemblies. Most external field assemblies do not require closed-loop control however, methods like magnetic robots and manipulation of individual components to target locations with external fields require manual or closed-loop control systems. 

The system being described in Figure 2-3 is a Kalman filter, a realtime controller consisting of several loops implementing matrix multiplication and other operations. The input to the system is the y array, and the output is the v array. First to be described are the carriers that will take part in the computation. Second, the procedures that specify the actions on the variables are listed. In this case, there is only one procedure (filt) consisting of several nested, labeled blocks and repeat loops. The "Imain)" qualifier indicates that filt is the starting point for execution. A quote mark (") indicates a hexadecimal constant, labeled blocks are named with a colon-equal ( =), and the is the binary concatenation operator. 

Wang, J. (2008). Air fraction estimation for multiple combustion mode diesel engines with dual-loop EGR systems. Control Engineering Practice 16 1479-1486. 

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