Control manipulated variables

In the sequential strategy, a control (manipulated) variable profile is discretized over a time interval. The discretized control profile can be represented as a piecewise constant, a piecewise linear, or a piecewise polynomial function. The parameters in such functions and the length of time subinterval become decision variables in optimization problem. This strategy is also referred to a control vector parameterization (CVP). 

Complicated process control structure. Consider the example shown in Figure 5.22. A number of elementary questions arise with regard to this relatively complicated control structure. For example, how did we choose that the hot stream is not the effective control (manipulated) variable for the control of the level (rather than the control of the temperature) In more general... 

In the dynamic optimization algorithm depicted in Figure 10, a control parameterization technique (44) is used to discretize the originally continuous control variables. That is, a control (manipulative) variable u t) is represented by a set of piece-wise constants, , /= 1, 2,. .., q. These constants are treated as parameters to be determined by using dynamic optimization algorithms. 

Controlled Manipulated Variable Manipulated Variable Manipulated... 

In order to operate a process facility in a safe and efficient manner, it is essential to be able to control the process at a desired state or sequence of states. This goal is usually achieved by implementing control strategies on a broad array of hardware and software. The state of a process is characterized by specific values for a relevant set of variables, eg, temperatures, flows, pressures, compositions, etc. Both external and internal conditions, classified as uncontrollable or controllable, affect the state. Controllable conditions may be further classified as controlled, manipulated, or not controlled. Excellent overviews of the basic concepts of process control are available (1 6). 

Some of the inherent advantages of the feedback control strategy are as follows regardless of the source or nature of the disturbance, the manipulated variable(s) adjusts to correct for the deviation from the setpoint when the deviation is detected the proper values of the manipulated variables are continually sought to balance the system by a trial-and-error approach no mathematical model of the process is required and the most often used feedback control algorithm (some form of proportional—integral—derivative control) is both robust and versatile. 

The feedforward control strategy (Fig. lb) addresses the disadvantages of the feedback control strategy. The feedforward control strategy measures the disturbance before it affects the output of the process. A model of the process determines the adjustment ia the manipulated variables(s) to compensate for the disturbance. The information flow is therefore forward from the disturbances, before the process is affected, to the manipulated variable iaputs. 

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. 

Stea.dy-Sta.teFeedforwa.rd, The simplest form of feedforward (FF) control utilizes a steady-state energy or mass balance to determine the appropriate manipulated variable adjustment. This form of feedforward control does not account for the process dynamics of the disturbance or manipulated variables on the controlled variable. Consider the steam heater shown ia Figure 15. If a steady-state feedforward control is designed to compensate for feed rate disturbances, then a steady-state energy balance around the heater yields ... 

Constraint control strategies can be classified as steady-state or dynamic. In the steady-state approach, the process dynamics are assumed to be much faster than the frequency with which the constraint control appHcation makes its control adjustments. The variables characterizing the proximity to the constraints, called the constraint variables, are usually monitored on a more frequent basis than actual control actions are made. A steady-state constraint appHcation increases (or decreases) a manipulated variable by a fixed amount, the value of which is determined to be safe based on an analysis of the proximity to relevant constraints. Once the appHcation has taken the control action toward or away from the constraint, it waits for the effect of the control action to work through the lower control levels and the process before taking another control step. Usually these steady-state constraint controls are implemented to move away from the active constraint at a faster rate than they do toward the constraint. The main advantage of the steady-state approach is that it is predictable and relatively straightforward to implement. Its major drawback is that, because it does not account for the dynamics of the constraint and manipulated variables, a conservative estimate must be taken in how close and how quickly the operation is moved toward the active constraints. 

An open-loop system positions the manipulated variable either manually or on a programmed basis, without using any process measurements. This operation is acceptable for well-defined processes without disturbances. An automanual transfer switch is provided to allow manual adjustment of the manipulated variable in case the process or the control system is not performing satisfac torily. 

A closed-loop system uses the measurement of one or more process variables to move the manipulated variable to achieve control. Closed-loop systems may include reedfoi ward, feedback, or both. 

Feedforward Control A reedfoi ward system uses measurements of disturbance vai iables to position the manipulated variable in such a way as to minimize any resulting deviation. The disturbance... 

On/Off Control An on/off controller is used for manipulated variables having only two states. They commonly control temperatures in homes, electric water-heaters and refrigerators, and pressure and liquid level in pumped storage systems. On7off control is satisfac-toiy where slow cychng is acceptable because it always leads to cycling when the load hes between the two states of the manipulated variable. The cycle will be positioned symmetrically about the set point only if the normal value of the load is equidistant between the two states of the manipulated variable. The period of the symmetrical cycle will be approximately 40, where 0 is the deadtime in the loop. If the load is not centered between the states of the manipulated variable, the period will tend to increase, and the cycle follows a sawtooth pattern. 

A three-state controller is used to drive either a pair of independent on/off actuators such as heating and cooling valves, or a bidirectional motorized actuator. The controller is actually two on/off controllers, each with deadband, separated by a dead zone. When the controlled variable lies within the dead zone, neither output is energized. This controller can drive a motorized valve to the point where the manipulated variable matches the load, thereby avoiding cychng. 

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 ... 

Feedforward Control If the process exhibits slow dynamic response and disturbances are frequent, then the apphcation of feedforward control may be advantageous. Feedforward (FF) control differs from feedback (FB) control in that the primary disturbance or load (L) is measured via a sensor and the manipulated variable (m) is adjusted so that deviations in the controlled variable from the set point are minimized or eliminated (see Fig. 8-29). By taking control action based on measured disturbances rather than controlled variable error, the controller can reject disturbances before they affec t the controlled variable c. In order to determine the appropriate settings for the manipulated variable, one must develop mathematical models that relate ... 

The Smith predictor is a model-based control strategy that involves a more complicated block diagram than that for a conventional feedback controller, although a PID controller is still central to the control strategy (see Fig. 8-37). The key concept is based on better coordination of the timing of manipulated variable action. The loop configuration takes into account the facd that the current controlled variable measurement is not a result of the current manipulated variable action, but the value taken 0 time units earlier. Time-delay compensation can yield excellent performance however, if the process model parameters change (especially the time delay), the Smith predictor performance will deteriorate and is not recommended unless other precautions are taken. 

Selective and Override Control When there are more controlled variables than manipulated variables, a common solution to this problem is to use a selector to choose the appropriate process variable from among a number of available measurements. Selec tors can be based on either multiple measurement points, multiple final control elements, or multiple controllers, as discussed below. Selectors are used to improve the control system performance as well as to protect equipment from unsafe operating conditions. 

Other types of selective systems employ multiple final control elements or multiple controllers. In some applications, several manipulated variables are used to control a single process variable (also called split-range control). Typical examples include the adjustment of both inflow and outflow from a chemic reactor in order to control reactor pressure or the use of both acid and base to control pH in waste-water treatment. In this approach, the selector chooses from several controller outputs which final control element should be adjusted (Marlin, Process Control, McGraw-Hill, New York, 1995). 

In continuous processes where automatic feedback control has been implemented, the feedback mechanism theoretically ensures that product quality is at or near the set point regardless of process disturbances. This, of course, requires that an appropriate manipulated variable has been identified for adjusting tne product quality. However, even under feedback control, there may be daily variations of product quahty because of disturbances or equipment or instrument malfunctions. These occurrences can be analyzed using the concepts of statistical quahty control. 

Three examples of simple multivariable control problems are shown in Fig. 8-40. The in-line blending system blends pure components A and B to produce a product stream with flow rate w and mass fraction of A, x. Adjusting either inlet flow rate or Wg affects both of the controlled variables andi. For the pH neutrahzation process in Figure 8-40(Z ), liquid level h and the pH of the exit stream are to be controlled by adjusting the acid and base flow rates and w>b. Each of the manipulated variables affects both of the controlled variables. Thus, both the blending system and the pH neutralization process are said to exhibit strong process interacHons. In contrast, the process interactions for the gas-liquid separator in Fig. 8-40(c) are not as strong because one manipulated variable, liquid flow rate L, has only a small and indirec t effect on one controlled variable, pressure P. 

Strong process interacHons can cause serious problems if a conventional multiloop feedback control scheme (e g., PI or PID controllers) is employed. The process interacHons canproduce undesirable control loop interac tions where the controllers fight each other. Also, it may be difficult to determine the best pairing of controlled and manipulated variables. For example, in the in-hne blending process in Fig. 8-40(<7), should w be controlled with and x with tt>g, or vice versa ... 

Choose different controlled or manipulated variables (or pair-... 

The selection of controlled and manipulated variables is of crucial importance in designing a control system. In particular, a judicious choice may significantly reduce control loop interactions. For the blending process in Fig. 8-40(d ), a straightforward control strategy would be to control x by adjusting w, and w by adjusting Wg. But... 

As an illustrative example, consider the simplified block diagram for a representative decoupling control system shown in Fig. 8-41. The two controlled variables Ci and Co and two manipulated variables Mi and Mo are related by four process transfer functions, Gpn, Gpi9, and pie, Gpii denotes the transfer function between Mi... 

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