Cascade control is a control in which two or more control loops are connected so that the output of one controller corrects the setpoint of the other controller.
The figure above is a block diagram that illustrates the concept of cascade control. The blocks in the diagram actually represent the components of two control loops: the master loop, which is made up of control system elements A, E, F, and G, and the slave loop, which is made up of control system elements A, B C, and D. The controller output of the master loop is the reference (setpoint) for the slave controller. The slave loop controller generates a control signal for the actuator.
For processes that have significant lag characteristics (capacitance or resistance that slows down changes in the variable), the cascade system's slave control loop can detect the process error earlier and thus reduce the time required to correct the error. We can say that the slave control loop "divides" the delay and reduces the impact of the disturbance on the process.
A cascade control system uses more than one primary sensing element and the controller (in the slave control loop) receives more than one input signal. Therefore, the cascade control system is a multi-loop control system.
Example of a cascade control system
In the example above, the control loop will eventually be the leading loop when building a cascade control system. The slave circuit will be added later. The purpose of this process is to heat the water passing through the interior of the heat exchanger by flowing around the pipes through which the steam flows. One of the features of the process is that the heat exchanger body has a large volume and contains a lot of water. A large amount of water has a capacity that allows you to store a large amount of heat. This means that if the temperature of the water entering the heat exchanger changes, these changes will appear at the exit of the heat exchanger with a large delay. The reason for the delay is the large capacitance. Another feature of this process is that the steam pipes resist the transfer of heat from the steam inside the pipes to the water outside the pipes. This means that there will be a delay between changes in steam flow and corresponding changes in water temperature. The reason for this delay is resistance.
The primary element in this control loop controls the temperature of the water leaving the heat exchanger. If the leaving water temperature changes, the corresponding physical changes in the primary element are measured by the transmitter, which converts the temperature value into a signal sent to the controller. The controller measures the signal, compares it with the setpoint, calculates the difference and then generates an output signal that controls the control valve on the steam line, which is the final element of the control loop (regulator). The steam control valve either increases or decreases the steam flow to bring the water temperature back to the set point. However, due to the lag characteristics of the process, the change in water temperature will be slow and it will take a long time before the control loop can sense how much the water temperature has changed. By then, too much change in water temperature may have occurred. As a result, the control loop will generate an excessively strong control action, which can lead to a deviation in the opposite direction (overshoot), and will again "wait" for the result. Due to a slow response like this, the water temperature can cycle up and down for a long time before it settles back to the set point.
The transient response of the control system is improved when the system is supplemented with a second cascaded control loop, as shown in the figure above. The added loop is the cascade control slave loop.
Now, when the steam flow changes, these changes will be read by the flow sensor (B) and measured by the transmitter (C), which sends a signal to the slave controller (D). At the same time, the temperature sensor (E) in the lead control loop senses any change in the temperature of the water leaving the heat exchanger. These changes are measured by a measuring transducer (F), which sends a signal to the master regulator (G). This controller performs the functions of measurement, comparison, calculation and produces an output signal that is sent to the slave controller (D). This signal corrects the setpoint of the slave controller. The slave controller then compares the signal it receives from the flow sensor (C) with the new setpoint, calculates the difference and generates a correction signal which is sent to the control valve (A) to correct the steam flow.
In a control system with the addition of a slave control loop to the main loop, any change in steam flow rate is immediately read by the additional loop. The necessary adjustment is made almost immediately, before the perturbation from the steam flow affects the water temperature. If there have been changes in the water temperature at the outlet of the heat exchanger, the sensing element perceives these changes and the master control loop corrects the controller setpoint in the slave control loop. In other words, it sets a set point or "shifts" the controller in the slave control loop so as to adjust the steam flow in order to maintain the desired water temperature. However, this response of the slave controller to changes in steam flow reduces the time required to compensate for the effect of a disturbance from the steam flow.
When analyzing complex automatic control systems, their block diagrams are of particular importance, showing the points of application of influences and possible paths for the propagation of signals that interact between the elements of the system.
Block diagrams consist of the following structural elements:
dynamic, carrying out some functional or operator connection between their input and output signals;
transforming, serving to transform the nature or structure of signals;
comparisons in which signals are subtracted or added;
branch points, in which the signal propagation path branches into several paths leading to different points in the system;
connections or lines of the block diagram indicating the direction of signal propagation;
points of application of influences;
logical, performing logical operations.
We indicated above that any automatic control system, according to the very principle of its operation, always
has at least one feedback, which serves to compare the actual and required value of the controlled variable. We agreed to call this kind of feedback the main one.
However, it should be noted that modern automatic control systems, in addition to the main feedbacks, the number of which is equal to the number of controlled variables, often have several more auxiliary or local feedbacks. Automatic control systems with one controlled variable, having only one main feedback and no local feedback, are called single-loop. In single-loop systems, an action applied to any point can bypass the system and return to the original point, following only one detour path (see Fig. II.8). Automatic control systems that, in addition to one main feedback, have one or more main or local feedbacks are called multi-loop. Multiloop systems are characterized by the fact that in them the action applied to any point can bypass the system and return to the original point, following several different bypass paths.
As an example of a multi-loop (two-loop) automatic control system with one controlled variable, one can cite a servo system in which, in addition to the main feedback that serves to generate an error signal and is carried out using a synchro-sensor and a synchro-receiver, there is also local feedback; the latter is carried out using a tachogenerator and an RC circuit connected to it, the voltage from the output of which is subtracted from the error signal.
An example of a multi-loop, multiple variable control system is an aircraft engine control system, in which the controlled variables may be engine speed, boost pressure, ignition timing, oil temperature, coolant temperature, and other variables.
The reasons for introducing local feedback into the automatic control system are very different. So, for example, they are used in corrective elements to convert the signal in accordance with the required control law, in amplifying elements - for linearization, noise reduction, lowering the output resistance, in actuators - to increase power.
Feedback covering several series-connected elements of the system can be introduced to give them the required dynamic properties.
Multidimensional automatic control systems, i.e. systems with several controlled variables, subdivide
on systems of uncoupled and coupled regulation.
Systems of uncoupled regulation are those in which regulators designed to regulate various quantities are not connected with each other and can only interact through a common object of regulation for them. Systems of uncoupled regulation, in turn, can be divided into dependent and independent.
Dependent systems of uncoupled control are characterized by the fact that in them the change in one of the controlled quantities depends on the change in the others. As a result, in such systems, the processes of regulation of various controlled variables cannot be considered independently, in isolation from each other.
An example of a dependent system of uncoupled control is an aircraft with an autopilot, which has independent control channels for the rudders. Suppose, for example, that the aircraft has deviated from a predetermined course. This will cause rudder deflection due to the presence of the autopilot. When returning to a given course, the angular velocities of both bearing surfaces of the aircraft, and, consequently, the lift forces acting on them, will become unequal, which will cause the aircraft to roll. The autopilot will then deflect the ailerons. As a result of deviations of the rudder and ailerons, the drag of the aircraft will increase. Therefore, it will begin to lose height, and its longitudinal axis will deviate from the horizontal. The autopilot will then deflect the elevator.
Thus, in the considered example, the control processes of the three controlled variables - heading, lateral roll and longitudinal roll - strictly speaking, cannot be considered independent of each other, despite the presence of independent control channels.
An independent system of uncoupled control is characterized by the fact that in it the change in each of the controlled quantities does not depend on the change in the others, so that the processes of regulation of various quantities can be considered in isolation from each other. As an example of independent systems of uncoupled regulation, one can often consider a system for regulating the number of revolutions of a hydroturbine and a system for regulating the voltage of a synchronous generator rotated by it. The control processes in these systems are independent, due to the fact that the voltage control process usually proceeds many times faster than the speed control process.
Systems of coupled regulation are such systems in which regulators of various regulated values have mutual connections with each other, which interact between them outside the object of regulation.
A coupled control system is called autonomous if the connections between its constituent regulators
are such that a change in one of the controlled variables during the control process does not cause a change in the remaining controlled variables.
The block diagram of the system of incoherent control of a two-dimensional object has the form:
Regulation error
Control action
Measured controlled variables
Unmeasured outputs on the main channels with transfer function and
Controllers with transfer functions and
Using the discrete transfer functions of the controllers of the main and cross channels, we describe the system of non-coupled control:
Let us transform system (2.0) by substitution, obtaining the equation of the connection between the system outputs and its inputs
(2.2)
In the first equation, we substitute the right side of the second equation instead:
(2.3)
Similarly, when substituting into the second equation instead of the right side of the first equation, you can get the dependence of the output on and .
Equation (2.3) shows that each controlled variable depends both on the first input of the system , and on the second input of the system . Let us show that the stability of an uncoupled system decreases in this case. To do this, we assume that the transfer functions of the object in the main and cross channels are equal to each other and the transfer functions of the controllers are equal to each other.
Then equation (2.3) takes the form:
(2.4)
If there are no cross-links in the object, then the output value depends only on the reference in accordance with the following expression:
In accordance with the Nyquist criterion, in order for a closed single-loop system to be stable (if an open one is stable), it is necessary that the APFC hodograph of an open system does not cover a point with coordinates . Based on this, in an incoherent control system, if taken equal to zero, this criterion will be the same, with the only difference that the coordinates of the critical point will be . Thus, in an incoherent control system, the area of stable control narrows, which reduces the stability of the system and worsens the quality of the transition process. If internal cross-couplings are not taken into account when calculating the optimal controller settings in an incoherent control system, then the system may be unstable. In order to maintain the stability of the system of incoherent control in the presence of internal links, it is necessary to reduce the gain compared to the gains of the controllers in the absence of cross-links by so much that the AFC hodograph of the open system does not cover the point with coordinates .
Obviously, this can be achieved by significantly achieving the controller gain, i.e. the speed of the regulator, which sharply worsens the quality of regulation. Therefore, with strong internal connections, the opportunity to obtain a high quality of regulation should be sought not in adjusting the structures and settings of unrelated regulators, but by “untying” internal connections through cross channels. Those. it is necessary to change the structure of the system itself. There are two ways to weaken or completely “untie” cross-links:
1. choosing unrelated or weakly related parameters as controlled values;
2. creation of a system of linked regulation by introducing additional external compensating links between regulators into the ACP
An uncoupled control system is simpler, more reliable and cheaper than a coupled control system. They are realizable even in cases where coherent regulation systems are technically unfeasible. However, they are susceptible to disturbing influences, propagate through the main and cross channels, which can lead to a deterioration in the quality of regulation and, as the best option, loss of stability. The advantages of incoherent control systems make it necessary to look for ways to extend the scope of their application to objects with interconnected controlled values while maintaining a satisfactory quality of control. The degree of connection between the two controlled variables can be determined using the transfer functions of the object in the main and cross channels. The degree of communication on the first main channel is equal to the ratio of its transfer function to the transfer function of the second main channel: . The degree of communication on the second cross channel is equal to the ratio of the transfer function of this channel to the transfer function of the first main channel: . The general degree of connection between the regulating values: . Depending on the magnitude of the overall degree of connection, one of the following control options can be recommended:
With such a connection of the regulators, the channels will become the main ones and the overall degree of connection will be characterized by a new value. If it turns out that the total degree of correlation of values is less than 1, then a system of decoupled control can be applied;
3. at the ratio , the degree of connection is significant, which can significantly reduce the stability of the system of incoherent regulation; in this case, it is necessary to eliminate or significantly weaken the internal ties in the ACP;
4. It is possible to “untie” the regulation of values in the presence of cross-links if the regulation of values with different dynamic characteristics is carried out, which reduces their relationship through the process, for example, pressure regulators usually operate at higher frequencies than temperature regulators, which determines their weak mutual influence Each other.
Approaches to setting up an incoherent control system can be as follows:
1. setting in single-circuit systems;
2. Simultaneous optimization of regulators in the system of incoherent regulation, taking into account the influence of the main and transitional channels.
The first approach uses models of the main channels and the corresponding regulators. Of these, single-loop control systems are composed, in which the adjustment of the corresponding controllers is carried out by one of the numerical methods. The advantage of this approach to setting up regulators is simplicity and high speed.
It follows from the system of equations for the relationship between the plant outputs ( and ) and the system inputs ( and ) (2.3), (2.4) that the controlled value depends not only on the dynamic properties of the main channel and the controller , but also on the dynamic properties of the second main channel , cross channels , and from the second regulator. Similarly, the parameter. Therefore, the tuning of the control part of the system must be carried out taking into account the dynamic properties not only of the corresponding main channel, but also taking into account the influence of the dynamics of the cross channels. Therefore, the disadvantage of this approach to adjusting the controllers is the non-optimality of the resulting tuning parameters.
Let's consider the second approach. The calculation of the transient process in the system of incoherent control is carried out according to the following system of finite-difference equations:
, where weight coefficients for which the following conditions are satisfied:
Quality indicators for the corresponding system output, used as optimization criteria. The larger of the weighting factors is assigned to the quality indicator of the output whose regulation is most important.
When using convolution, the optimization problem is formed as follows: 
. When using the gradient method as a numerical optimization method, the optimization algorithm (algorithm scheme) will be the same as for a single-loop system. The difference will be that when calculating the transient process, the system of equations (3.0) and the initial conditions (3.1) will be used. When calculating the partial derivatives of the criterion with respect to optimal settings, one of the two approaches discussed above can be used (with and without quasi-analytical recurrent dependencies). When using finite-difference equations, it is necessary to take partial derivatives of all equations of system (3.0) with respect to all settings of both controllers. The initial conditions for calculating the numerical values of the resulting system of finite-difference equations must be specified similarly to the initial conditions (3.1).
2. Classification of ASR. Management principles.
Control- this is a purposeful impact on the object, which ensures its optimal (in a certain sense) functioning and is quantified by the value of the quality criterion (indicator). The criteria may be of a technological or economic nature (performance of a process unit, production cost, etc.).
During operation, the output values deviate from the set values due to disturbances z B and there is a mismatch between the current at T and given and 3 object output values. If available disturbances z B the object independently ensures normal functioning, i.e. independently eliminates the resulting mismatch at T-and 3, then it does not need to be controlled. If the object does not ensure the fulfillment of the conditions for normal operation, then to neutralize the influence of disturbances, it is imposed control action x R, changing the material or heat flows of the object with the help of the actuator. Thus, in the process of control, the object is subjected to influences that compensate for disturbances and ensure the maintenance of its normal operation.
regulationcalled maintaining the output values of the object near the required constant or variable values in order to ensure the normal mode of its operation by applying control actions to the object.
An automatic device that maintains the output values of an object near the required values is called automatic regulator.
According to the principle of regulation ASR is divided into those operating by deviation, by disturbance and by the combined principle.
By deviation. In systems operating on the deviation of the controlled value from the set value (Fig. 1-2, a), outrage z causes a deviation of the actual value of the controlled variable at from its given value and. The automatic controller AP compares the values u and i, in case of their mismatch, it produces a regulatory effect X of the corresponding sign, which is fed through the actuator (not shown in the figure) to the regulated object of the OR, and eliminates this mismatch. In deviation control systems, mismatch is necessary for the formation of regulatory actions, this is their disadvantage, since the task of the regulator is precisely to prevent mismatch. However, in practice, such systems have received predominant distribution, since the regulatory action in them is carried out regardless of the number, type and place of occurrence of disturbing influences. Deviation control systems are closed.
Out of indignation. When regulating by disturbance (Fig. 1-2, b) AP B regulator receives information about the current value of the main disturbing action z1. When measuring it and not matching with nominal value and B the regulator generates a regulatory action X, directed to the object. In perturbed systems, the control signal passes through the loop faster than in systems based on the principle of deviation, as a result of which the perturbing effect can be eliminated even before the mismatch occurs. However, it is practically impossible to implement disturbance control for most objects of chemical technology, since this requires taking into account the influence of all object disturbances ( z1, z2, ...) whose number is usually large; moreover, some of them cannot be quantified. For example, the measurement of such perturbations as a change in catalyst activity, the hydrodynamic situation in the apparatus, the conditions of heat transfer through the heat exchanger wall, and many others encounters fundamental difficulties and is often unfeasible. Usually, the main perturbation is taken into account, for example, by the load of the object.
In addition, signals about the current value of the controlled variable are sent to the control loop of the system by disturbance. at are not received, therefore, over time, the deviation of the controlled value from the nominal value may exceed the permissible limits. Disturbance control systems are open.
According to the combined principle. With such regulation, i.e., with the joint use of the principles of regulation by deviation, and by disturbance (Fig. 1-6, in), it is possible to obtain high-quality systems . In them, the influence of the main perturbation z1 is neutralized by the AR B regulator, which operates on the perturbation principle, and the influence of other perturbations (for example, z2 etc.)-regulator AR, reacting to the deviation of the current value of the reacted quantity from the set value.
According to the number of adjustable values ASR is divided into one-dimensional and multidimensional. One-dimensional systems have one adjustable value, the second - several adjustable values.
In its turn multidimensional systems can be divided into systems of uncoupled and coupled regulation. In the first of them, the regulators are not directly related to each other and affect the object of regulation common to them separately. Systems unrelated controls are usually used when the mutual influence of the controlled values of the object is small or practically absent. Otherwise, systems are used related regulation, in which regulators of different values of one technological object are interconnected by external links (outside the object) in order to weaken the mutual influence of the controlled values. If at the same time it is possible to completely eliminate the influence of the controlled variables on one another, then such a system of coupled control is called autonomous.
By the number of signal paths ASR is divided into single-circuit and multi-circuit. Single-loop are called systems containing one closed loop, and multiloop- having several closed circuits
By appointment(the nature of the change in the driving influence) ASR are divided into automatic stabilization systems, program control systems and servo systems.
Automatic stabilization systems designed to maintain the controlled value at a given value, which is set constant ( u= const). These are the most common systems.
Program control systems constructed in such a way that the set value of the controlled variable is a function of time known in advance u=f(t). They are equipped with software sensors that form the value and in time. Such systems are used in the automation of chemical-technological processes of periodic action or processes operating according to a certain cycle.
In tracking systems the set value of the controlled variable is not known in advance and is a function of an external independent process variable u=f(y 1). These systems serve to control one technological quantity ( slave), which is in a certain dependence on the values of another ( leading) technological value. A variety of tracking systems are systems for regulating the ratio of two quantities, for example, the consumption of two products. Such systems reproduce at the output a change in the driven value in a certain ratio with a change in the leading one. These systems seek to eliminate the mismatch between the value of the leading quantity, multiplied by a constant factor, and the value of the driven quantity.
By the nature of regulatory influences Distinguish between continuous ACP, relay and pulse.
Continuous ACPconstructed in such a way that a continuous change in the input value of the system corresponds to a continuous change in the value at the output of each link.
Relay (position) ACP have a relay link that converts a continuous input value into a discrete relay value that takes only two fixed values: the minimum and maximum possible. Relay links allow you to create systems with very high gains. However, in a closed control loop, the presence of relay links leads to self-oscillations of the controlled value with a certain period and amplitude. Systems with position controllers are relay systems.
Pulse ACPhave in their composition a pulse link that converts a continuous input value into a discrete pulse, i.e. into a sequence of pulses with a certain period of their alternation. The period of appearance of pulses is set forcibly. The input value is proportional to the amplitude or duration of the output pulses. The introduction of a pulse link frees the measuring device of the system from the load and allows the use of a low-power, but more sensitive measuring device at the output, which responds to small deviations of the controlled value, which leads to an increase in the quality of the system.
In the pulse mode, it is possible to build multi-channel circuits, while reducing the energy consumption for actuating the actuator.
Systems with a digital computing device in a closed control loop also operate in a pulsed mode, since the digital device outputs the result of the calculation in the form of pulses following at certain time intervals necessary for the calculation. This device is used when the deviation of the controlled variable from the set value must be calculated from the readings of several measuring instruments or when, in accordance with the criteria for the best performance of the system, it is necessary to calculate the program for changing the controlled variable.
Connecting the units according to the uncoupled control scheme ensures the independence of the operation of both units, i.e., changing the water flow for hot water supply over a wide range from zero (at night) to the maximum has practically no effect on the operation of the heating system.
To do this, the water flow in the supply line must be equal to the total water flow for heating - ventilation and hot water supply. Moreover, the water consumption for DHW should be taken according to the maximum load of hot water supply and the minimum temperature of the water in the supply line, i.e. in the mode when the DHW load is completely covered from the supply line (if the consumer does not have storage tanks installed).
Water consumption for heating, ventilation, hot water supply and total water consumption by each network subscriber does not depend on the network configuration. The calculated flow rate by the subscriber is set using a throttle diaphragm, the hole diameter of which is determined by the formula (clause 4.17 of SP 41-101-95)
where G is the estimated water flow in the pipeline, equal to Gtotal t / h
DN - pressure quenched by the diaphragm, m
Minimum diaphragm opening size - 3 mm
Make-up system automation
Automated make-up devices maintain a constant or changing water pressure according to a certain law at the network make-up point.
For heating networks with relatively small pressure losses in the mains and a favorable terrain profile, the pressure at the make-up point in all modes (including the mode when the network pumps are stopped) is maintained constant. It is envisaged to maintain a constant pressure in the return manifold in front of the network pumps with the help of a pressure regulator “after itself (feed-up regulator) installed on the make-up water pipeline.
In the case when the static pressure of the heating network exceeds the pressure in the return manifold of the boiler house during the operation of the network pumps, the adjustment to the static pressure is carried out manually. Water pressure is measured in the pressure pipes of the make-up pumps by local indicating and signaling pressure gauges, which give an impulse to turn on the backup pump, and in the return manifold by indicating, self-recording and signaling pressure gauges on the local shield. It is also envisaged to install a secondary device indicating, recording and signaling a flow meter for measuring the consumption of make-up water and a secondary device for recording and signaling an oxygen meter for measuring the oxygen content in make-up water at the local shield. The resistance thermometer on the make-up line is connected to a common recorder, which simultaneously records the temperature of the network water.
In open heating networks, when installing central storage tanks, the pressure in the return pipeline is automatically regulated by two control valves, of which the first is installed on the bypass pipeline of excess network water to the storage tanks, and the second on the pipeline from the storage tanks after transfer pumps. During hours when the load of hot water supply is below the daily average, the transfer pumps are turned off, and the pressure in the return pipeline is regulated by the first valve. At hours when the hot water supply load is higher than the average daily load, the transfer pumps are automatically turned on, the first control valve is closed, and the pressure regulator switches to the control valve installed after the transfer pumps.
To ensure a constant flow of make-up water in an open heating network, a flow regulator is installed on the pressure pipeline of the make-up pumps.
The water level in the make-up deaerator tank is maintained by a control valve on the chemically treated water line. If an atmospheric deaerator is used instead of a sliding pressure vacuum deaerator, then a regulator is additionally installed to maintain a constant pressure in the deaerator column. The scheme provides for an emergency stop of the working ones: make-up and transfer pumps and automatic switching on of the backup ones, as well as signaling the pressure in the return pipeline of the level in the make-up deaerator tank and storage water tanks and the oxygen content in the make-up water.
