Oscillatory control

Saunders, G.W., and T.A. Storch. 1971. Coupled oscillatory control mechanism in a planktonic... 

Changing an input variable in one direction can produce small changes in product composition, while changing it in the other direction can produce very large changes in product composition. This asymmetric behavior of the steady-state gains can result in sluggish control in one direction and oscillatory control in the other direction. 

As more tanks are added to the system, the control becomes more difficult. Controlling T with Q (we call this a first-order system) is easy the system is never oscillatory. Controlling Tj with Q (a second-order system) gives some oscillatory behavior, but controller gains have to be quite large before the oscillation... 

The gel point in materials represents the point where behavior changes from viscous (liquid-like) to elastic (solid-like). The conditions under which this occurs are critical to such food constituents as wheat-soya solutions used as setting agents within reconstituted meat products. In this case, oscillatory-controlled stress experiments, in which a small sinusoidal stress is applied to the material, provide a convenient method for evaluating elastic and viscous properties without destroying the delicate structure of soft semisolids. 

These results illustrate that with the lower performance specification (Td — 2), there is little difierence between the PI and PID performance. However, for the higher performance specifications (rd = 1 and 0.67), the PID performance is superior in that it produces less oscillatory control signal and process output responses. 

Oscillatory control loops are often the result of either (i) a yclic process disturbance, (ii) a sticking control valve, or iii) a poorly tuned controller. A simple test can be used to listinguish between Case (i), and Cases (ii) and (iii). If the controller is placed in the manual mode for a short period of time and the oscOlations die out, then the oscillation is... 

The next problem to consider is how chaotic attractors evolve from tire steady state or oscillatory behaviour of chemical systems. There are, effectively, an infinite number of routes to chaos [25]. However, only some of tliese have been examined carefully. In tire simplest models tliey depend on a single control or bifurcation parameter. In more complicated models or in experimental systems, variations along a suitable curve in the control parameter space allow at least a partial observation of tliese well known routes. For chemical systems we describe period doubling, mixed-mode oscillations, intennittency, and tire quasi-periodic route to chaos. 

Specific Commercial Rotational Viscometers. Information on selected commercial rotational viscometers can be found ia Table 7. The ATS RheoSystems Stresstech rheometer is an iastmment that combines controlled stress as well as controlled strain (shear rate) and oscillatory measurements. It has a torque range of 10 to 50 mN-m, an angular velocity range of 0 to 300 rad/s, and a frequency range of seven decades. Operation and temperature programming (—30 to 150°C higher temperatures optional) are computer controlled. 

Haake has introduced other viscometers, including the RheoStress RSlOO, which offers controlled stress as well as controlled shear rate and oscillatory modes over a temperature range of —50 to 350°C (ambient to 500°C is also possible). This versatile viscometer covers a shear rate range of 10 ... 

Rajamani and Herbst (loc. cit.) compared control of an experimental pilot-mill circuit using feedback and optimal control. Feedback control resulted in oscillatory behavior. Optimal control settled rapidly to the final value, although there was more noise in the results. A more complete model should give even better results. 

These phenomena are being actively studied at the present time, and constitute a new chapter in the theory of oscillations that is known as piecewise linear oscillations. There exists already a considerable literature on this subject in the theory of automatic control systems11-34 but the situation is far from being definitely settled. One can expect that these studies will eventually add another body of knowledge to the theory of oscillations, that will be concerned with nonanalytic oscillatory phenomena. 

A promising approach toward controlling the static and impact sensitivity of initiators has consisted of co-precipitating the primary ex pi on a carrier or doping it in a manner which affects its solid state characteristics (Ref 97) Oscillatory Reactions... 

In this short initial communication we wish to describe a general purpose continuous-flow stirred-tank reactor (CSTR) system which incorporates a digital computer for supervisory control purposes and which has been constructed for use with radical and other polymerization processes. The performance of the system has been tested by attempting to control the MWD of the product from free-radically initiated solution polymerizations of methyl methacrylate (MMA) using oscillatory feed-forward control strategies for the reagent feeds. This reaction has been selected for study because of the ease of experimentation which it affords and because the theoretical aspects of the control of MWD in radical polymerizations has attracted much attention in the scientific literature. 

Microbial kinetics can be quite complex. Multiple steady states are always possible, and oscillatory behavior is common, particularly when there are two or more microbial species in competition. The term chemostat can be quite misleading for a system that oscillates in the absence of a control system. 

The oscillatory nature of the action and the offset make the resulting control rather imperfect, but the use of on/off control can be justified by its simplicity and low price, and the reasonable control obtained, especially for systems which respond slowly. 

The response of a controller to an error depends on its mode. In the proportional mode (P), the output signal is proportional to the detected error, e. Systems with proportional control often exhibit pronounced oscillations, and for sustained changes in load, the controlled variable attains a new equilibrium or steady-state position. The difference between this point and the set point is the offset. Proportional control always results in either an oscillatory behaviour or retains a constant offset error. 

This example shows that the reactor may oscillate, either naturally according to the system parameters, or by applied controller action. Owing to the highly non-linear behaviour of the system, it is sometimes found that the net yield from the reactor may be higher under oscillatory conditions than at steady state (see simulation examples OSCIL and COOL). It should be noted also that under controlled conditions, Tset need not necessarily be set equal to the steady-state value, T, and Tset, and that the control action may be used to force the reactor to a more favourable yield condition than that simply determined by steady-state balance considerations. 

We have not encountered examples with a second order equation, especially one that exhibits oscillatory behavior. One reason is that processing equipment tends to be self-regulating. An oscillatory behavior is most often a result of implementing a controller, and we shall see that in the control chapters. For now, this section provides several important definitions. 

We expect that a proportional controller will improve or accelerate the response of a process. The larger Kc is, the faster and more sensitive is the change in the compensation with respect to a given error. However, if Kc is too large, we expect the control compensation to overreact, leading to oscillatory response. In the worst case scenario, the system may become unstable. 

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