Proportional-time control

In systems where on off control produces a limit cycle that is both too long and too high, certain modifications may be applied. Proportional time control is a technique by which the on off output is modulated with a signal of fixed period but variable on time. The percentage of each period during which the controller output is maximum is proportional to deviation. Thus the average value of output is the same as it would be with a proportional controller. Figure 5.10 shows the relationship between deviation and controller output. 

It might be mentioned at this point that proportional time control of a constant speed motor is a practical and inexpensive system. Two outputs must again be provided, with a dead zone between. Both outputs are modulated with time proportioning, one for a positive error, the other for a negative. Offset is encountered in the two state loop, but the motor now overcomes it. Proportional time control with a constant-speed motor is essentially integral control, with a reset time of... 

The polysulfide impression materials can be formulated to have a wide range of physical and chemical characteristics by modifying the base (polysulfide portion), and/or the initiator system. Further changes may be obtained by varying the proportion of the base to the catalyst in the final mix. Characteristics varied by these mechanisms include viscosity control from thin fluid mixes to heavy thixotropic mixes, setting-time control, and control of the set-mbber hardness from a Shore A Durometer scale of 20 to 60. Variations in strength, toughness, and elasticity can also be achieved. 

Integral mode This improves on the proportional-only control by repeating the proportional action within a unit time while a deviation from set point exists. The regulating unit is only allowed to be at rest when set point and... 

The proportioning pump controls the rate of advancement, viz 10 inch/minute, of each sample through the analysis stream. Hence, a fixed length of tubing is equivalent to a fixed amount of time. Each analysis stream is made of transparent plastic flexible tubing, and each patient-sample is separated from one another by an air-bubble. 

Tray 4 temperature on the Lehigh distillation column i controlled by a pneumatic Pf controller with a 2-mipute reset time and a 50 percent proportional band. Temperature controller output (COr) adjusts the Ktpoint of a steam flow controller (reset time 0.1 min and proportional band 100 percent). Column base level is controlled by a pneumatic proportional-only controller setting bottoms product withdrawal rate. 

The equation describing a proportional-integral controller in the time... 

A diagonal proportional feedback controller is used with both gains set equal to. Time is in minutes. 

Figure 20. Isotherms and interface shapes for the time t = 1.0 for batchwise simulations of CZ growth. Results are shown for (a) uncontrolled, (b-d) integral control, and (e) proportional-integral control simulations. Isotherms are spaced as described for Figure 19. The figure is taken from Atherton et al. (153).

Calculate the behavior using this proportional feedback control with your choice of several different suitable values of the proportional gain Kp. Calculate and plot the change of height with time when this controller is used and find the final height for each Kp. Moreover, calculate the offset for each value of Kp. 

The implementation of the above distributed controllers stabilizes the fast dynamics and affords us the opportunity to carry out a numerical experiment Figure 3.7 shows the evolution of the product purity x2y, for the original system with the above proportional stabilizing controllers and starting from an initial condition slightly perturbed from the nominal steady state. Clearly, x2y, exhibits an initial fast transient ( boundary layer ) followed by a slow dynamics, highlighting the two-time-scale behavior of this process. 

A potential choice of manipulated inputs to address the control objectives in the slow time scale is [ 3 Mrsp]t, i.e., the product flow rate from the column reboiler, and the setpoint for the reactor holdup used in the proportional feedback controller of Equation (3.35). This cascade control configuration is physically meaningful as well intuitively, the regulation of the product purity 23 is associated with the conversion and selectivity achieved by the reactor, which in turn are affected by the reactor residence time. 

They are generally much faster than the chemical times and thus the chemical times control the equilibration process. The vibration relaxation time of H2 and 02 is of the order of 10"8 secs at combustion temperatures. The vibrational relaxation times decrease with temperature in proportion to exp (T-1/3). Further it is well established that the more complex the molecule the shorter the relaxation time. Thus for most propellant product mixtures the assumption that vibrational lags are not of concern, particularly when dissociation lags are present, is apparently a good one. 

Then the inventory loops are revisited. The liquid holdups in surge volumes are calculated so that the time constants of the liquid level loops (using proportional-only controllers) are a factor of 10 larger than the product-quality time constants. This separation in time constants permits independent tuning of the material-balance loops and the prod-... 

Initially use proportional-only controllers in all loops except flow7 controllers, where the normal tight tuning can be used K = 0.5 and T = 0.3 minutes). Set the gains in all level controllers (except reactors) equal to 2. Adjust the temperature, pressure, and composition controller gains by trial and error to see if you can line out the system with the proposed control structure. If P-only control cannot be made to work, PI will not w7ork either. When stable operation is achieved, add a little reset action to each PI controller (one at a time) to pull the process into the setpoint values. 

Within the enclosure, the 316 stainless steel reactor is sealed in a vacuum tight glass vessel at the bottom of which is a 5.08 cm window through which the incident and resultant laser beams pass. Up to 4 samples can be run at any time. The temperature in the reactor is controlled to 0.3°K at 800 K using a current proportional temperature controller [Honeywell UDC 5000]. The glass vessel containing the reactor is evacuated by a roughing pump initially, followed by a diffusion pump. 

A part of the analytical planning for a chemical complex is the setting up and maintenance of a sample library, where analyzed samples from each tank car load or reactor lot are stored for reference purposes. The retention time for these samples is set to exceed the probable delay between the time of product shipment and time of final consumption. Thus, if a customer is having difficulty with a particular batch of product, the retained samples enable the company to check the specifications and render rapid technical assistance. Reanalysis of the sample may also be used by the company to accept or reject claims regarding the quality of a product shipment. Thus, proportional process control, raw materials and product, analysis, sample retention, and careful record-keeping all comprise important parts of an operating chemical complex necessary for the maintenance of product quality and customer satisfaction. 

The control action described by eq. (11.36) is called proportional-integral control, because the value of the manipulated variable is determined by two terms, one of which is proportional to the error h, and the other proportional to the time integral of the error. 

Then the discrete-time control action produced by the proportional mode is... 

The temperature in one of the tanks (T, Tj,or T ) is controlled by a proportional temperature controller that manipulates the heat input (2i to the first tank. The disturbance is a drop in inlet feed temperature To from 90°F to 70°F at time 0 hours. Three different values of controller gain Kc = 2, 4, and 8) are used. 

The disturbance is a drop in inlet Feed temperature Tq from 90°F to 70°F at time = 0 hours. Proportional and proportional-integral controllers are used. The ODEs describing the system are... 

The openloop process transfer functions relating the manipulated and load variables (M and L) to the controlled variable (Y) are first-order lags with identical time constants (To) but with different gains Km and Kl). Derive equations for the closedloop steady-state error and the closedloop time constant for step disturbances in load if a proportional feedback controller is used. 

An openloop-unstable process has a transfer function containing a positive pole at -I- 1/t and a negative pole at — 1/ot. Its steady-state gain is unity. If a proportional-only controller is used, what is the value of a that gives a closedloop damping coefficient of 0.5 when the controller gain is 10 times the minimum gain ... 

A process has an openloop transfer function that is approximately a pure deadtime of D minutes. A proportional-derivative controller is to be used with a value of a equal to 0.1. What is the optimal value of the derivative time constant To Note that part of this problem involves defining what is meant by optimal. ... 

A process has an openloop transfer function relating controlled and manipulated variables that is a steady-state gain of unity and two first-order lags in series. The two time constants are 1 and 5 minutes. A proportional feedback controller is used. 

If a proportional analog controller is used, derive the relationships that show how the closedloop time constant Tcl and the closedloop damping coefficient CL vary with controller gain K,.. 

If a proportional digital controller is used with a zero-order hold and sampling time T. ... 

Proportional-Plus-Derivative Control. Here, derivative action is added to proportional controllers for processes with large capacitance and appreciable dead-time. Control action is now proportional to the rate of change (the time derivative) of the error signal. The response equation is written as... 

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