Time constant variable

Because of the time constants and dynamics associated with the top level s control and manipulated variables, setpoints are usually ramped incrementally to their new values in a manner such that the process is not disturbed and the proximity to constraints can be periodically checked before the next increment is made. 

Many misconceptions exist about cascade control loops and their purpose. For example, many engineers specify a level-flow cascade for every level control situation. However, if the level controller is tightly tuned, the out-flow bounces around as does the level, regardless of whether the level controller output goes direcdy to a valve or to the setpoint of a flow controller. The secondary controller does not, in itself, smooth the outflow. In fact, the flow controller may actually cause control difficulties because it adds another time constant to the primary control loop, makes the proper functioning of the primary control loop dependent on two process variables rather than one, and requites two properly tuned controllers rather than one to function properly. However, as pointed out previously, the flow controller compensates for the effect of the upstream and downstream pressure variations and, in that respect, improves the performance of the primary control loop. Therefore, such a level-flow cascade may often be justified, but not for the smoothing of out-flow. 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

Rate of change of /Input variable - Output Variable output variable / Process time constant /... 

The rate of change /Final value - Instantaneous value of the variable / Time constant /... 

In the end, analysis of vs 0 (the "classical" approach) is not quantitative, a problem we associate with surface area variability and ambiguity arising from the interpretation of P . To help determine which adsorption mechanism is operative, we turn to an alternative parameter, the IS impedance "time constant", T, which does not suffer from these drawbacks. 

Figures 3 and 4 were obtained using the steady state defined by the variables and parameters of Tables I and II. Table III shows the poles and time constants computed from the A matrix for this steady state.

It must be noted that although the calibration cell is very different from the adsorption cell [Fig. 18, cells (1) and (2)3, the heat capacity of both cells is not very different, as the similar values of the time constant of the calorimeter containing one cell or the other indeed show (350 sec in the case of the calibration cell and 400 sec in the case of the adsorption cell) (55). This is explained by the fact that in both eases, the calorimeter cell is almost completely filled with a metal. However, the glass tube which is immersed in the calorimeter cell and the pressure changes which occur in the course of the adsorption experiments may be the sources of variable thermal leaks. The importance of these leaks was appreciated by means of the following control experiments. 

Heater Calibration ratio (mW/mm) Mean deviation of results for variable thermal power (/iW/mm) Time constant (sec)... 

In the time constant (relaxation) method, the waveform of P is a negative step which produces a relaxation of the sample temperature from TB + ST to TB. The measure of P(T) may be critical when the power P is comparable with the spurious power or when the thermal conductance G is steeply variable with the temperature (i.e. G oc T3 in the case of contact conductances). 

Rate of change /Input variable — Output variable output variable J y Process time constant... 

Key to the Bauer model is an assumption that constant capital increases at a higher rate than variable capital - the former increases at 10 per cent per annum and the latter at 5 per cent (ibid. 67). The result is a continual increase in the organic composition of capital, the ratio of constant to variable capital. The rate of surplus value, the ratio of total surplus value to variable capital, is assumed to remain constant at all times. With variable capital increasing at 5 per cent each year, the same increase in the pool of total surplus value takes place, out of which additional increments of constant and variable capital are funded. Capitalist consumption is treated... 

The third block in Fig. 2.1 shows the various possible sensing modes. The basic operation mode of a micromachined metal-oxide sensor is the measurement of the resistance or impedance [69] of the sensitive layer at constant temperature. A well-known problem of metal-oxide-based sensors is their lack of selectivity. Additional information on the interaction of analyte and sensitive layer may lead to better gas discrimination. Micromachined sensors exhibit a low thermal time constant, which can be used to advantage by applying temperature-modulation techniques. The gas/oxide interaction characteristics and dynamics are observable in the measured sensor resistance. Various temperature modulation methods have been explored. The first method relies on a train of rectangular temperature pulses at variable temperature step heights [70-72]. This method was further developed to find optimized modulation curves [73]. Sinusoidal temperature modulation also has been applied, and the data were evaluated by Fourier transformation [75]. Another idea included the simultaneous measurement of the resistive and calorimetric microhotplate response by additionally monitoring the change in the heater resistance upon gas exposure [74-76]. 

J0i Use Laplace transforms to prove mathematically that a P controller produces steadystate ofiMt and that a PI controller does not. The disturbance is a step change in the load variable. The process openloop transfer functions, Gm and G[, are both liist-order lags with dUTerent gains but identical time constants. 

We are saying that we want the process to respond to a step change in setpoint as a first-order process with a closedloop time constant t,. The steadystate gain between the controlled variable and the setpoint is specified as unity, so there will be no offset. 

Draw a block diagram of a process that has two manipulated variable inputs (Mi and M]) that each affect the output (2T). A feedback controller Si is used to control X by manipulating Mi since the transfer function between Mj and X has a small time constant and smaU deadtime. 

A process consists of two transfer functions in series. The fint, relates the manipulated variable M to the variable and is a steady state gain of 1 and two filSt-order lags in series with equal time constants of 1 minute. 

The second,, relates Xi to the controlled variable and is a steadystate gain of 1 and a first-order lag with a time constant of S minutes. 

No a priori knowledge of the system time constants is needed. The method automatically results in a sustained oscillation at the critical frequency of the process. The only parameter that has to be specified is the height of the relay step. This would typically be set at 2 to 10 percent of the manipulated variable range. 

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