Laboratory 1

1. Automatic control systems design

Technological processes in industrial plants are complex combinations of physical, chemical, mechanical, etc., parallel or mixed processes. Performance analysis can be done by dividing the process in unitary, simple and independent processes and treat them separately taking into account the overall conditions in which the process unfolds. The control activity can be performed directly by a human operator manual control, or be performed as a combination of devices and functions which replace all or part of the operator - automatic or semi-automatic control. The most useful classification of automated process control can be done after the functional role of the system. Automatic monitoring systems: Provide automatically measuring, recording and primary processing of technological parameters values for the process. These systems, based on a series of devices with appropriate functions, provide the process operator with information about the progress and store data on plant history. Automatic signaling systems: Are based on the automatic control system, and they compare the measured values of process parameters with predetermined limits of normal operation (minimum and / or maximum) and uses optical and acoustic signals for exceeding predetermined limits, showing the place where they occurred. Automatic protection systems: Works with the signaling system and uses automatic locking devices to stop all or part of the facility, where certain parameters have reached dangerous limits of operation. Automatic control systems: Perform a series of operations according to a preset program with direct or remote control, with minimum consumption of power by the operator. The impulse to initiate the job can be given manually by the operator or automatically by a device or equipment. In this category of systems we have the starting and stopping systems (normal or emergency) for industrial processes (eg, start power units, coupling energy group to the system, etc.). Automatic control systems: Ensure a constant evolution or a change according to a given time law for the process variables. Advanced automatic control systems: Adaptive and optimal control which ensures not only automatic control but also the satisfaction of additional qualitative indicators (such as maximum efficiency, minimum cost, minimum consumption, etc.).

1.1 . Usual control structures

a) Monocontur control structure with output feedback

The feedback block diagram is shown in figure 1 where the execution element EE (actuator), the transducer T and the technological plant IT are lumped in together and form the fixed part of the control system. The elements in the block diagram are all continuous. The controller RA can be analogue (conventional) or digital and in this case additional elements of conversion A/D and D/A are necessary (dotted lines).

Fig. 1. Feedback control structure

These signals have the following interpretations: v(t) reference input e(t) error signal xc(t) command signal (actuating signal) xm(t) plant input w(t) external disturbance y(t) plant output and measured signal Control law xc(t) e (t) is usually implemented as a PID algorithm with existing design methods known and validated by practice. The main advantages of this structure are: low cost, simplicity in design and work efficiency. On the other hand there are many disadvantages. The most important is that at the occurrence of disturbances, the controller expects the output to modify and then sets off the effect of disturbance compensation. In the case of continuously variable disturbance, the system will be permanently in transient regime, the algorithm must ensure in this case a reduction in the amplitude of the

disturbed output. Actions to anticipate the effects of disturbances can be achieved only by implementing algorithms that are based on output derivatives. This can lead to a sudden command for actuators, that will not always be accepted for a particular category of equipments (eg vapor flow control at steam turbines, the flow control of gas compressors, etc.). This type of structure is recommended where the dynamic performance required for the system are modest.

b) Feedforward control structure

Figure 2 gives the traditional block diagram of a feedforward control system. Feedforward control can entirely eliminate the effect of the measured disturbance on the process output, and it is used whenever there is a major disturbance that can be measured before it affects the process output. According to this structure, the controller C2 is informed by the disturbance variation with a very small delay given only by the inertia of the sensor T2 and develops the control signal Xc2 by processing the error signal e2.

Fig. 2. Feedforward control structure

In this case the effect of the disturbance compensation generated by Xc2 is transmitted in parallel to the output W. The control scheme will be useful where the disturbance channel (W-Y) inertia is comparable to the channel W-Xp-e2-Y inertia. Otherwise on the compensation channel will have to introduce elements of anticipation or delay (through the control law C2) to equalize the information transfer time. If this is not done then we will disrupt the process even more. The controllers (C1,C2) parameters are determined so that the system ensures optimal response according to the input signal V (e1 error minimization) and the disturbance W, based on integral criteria.

c) Cascade control structure The block diagram of this structure is shown in figure 3. As the feedforward scheme this one allows the disturbance effect compensation before it is visible on the output.

Fig. 3. Cascade control structure

For this structure to be useful it is necessary to find in the process a measurable intermediate signal Y1 that changes faster than the output at the effect of disturbances, or otherwise, the disturbances change the output through the intermediate signal Y1. Transducer T2 senses the disturbance changes and sends this information to the controller C2, this will change the command signal Xm within the meaning of compensating the disturbance effect. Note that if the plant part IT1 inertia is greater than plant IT2 inertia, then the effect of the W1 disturbance and the compensation effect sent by C2 get to the output almost simultaneously, canceling each other. The C1 controller has the role of adjusting the output value and the compensation of disturbance effect that is applied directly to the IT1. In this way we have a more precise control, carried out in two steps, for the systems output signal Y. According to figure 3 the control structure provides the compensation of W1 disturbance effect and will work as a monocontur structure for the W disturbance (thus changing the output is expected before starting the disturbance rejection). Cascade control structure design is a complex problem and should be designed using logarithmic frequency characteristics, ensuring stability in comparison with the amplitude and phase.

d) Adaptive system structure

If the technological characteristics of the plant (transfer factors, time constants, etc.) changes over time then it is necessary to change the regulating law or the controller

parameters. If this change is made automatically by an adaptation device (DA) based on information received from the process, then the automatic system is called adaptive system whose block diagram is shown in figure 4.

Fig. 4. Adaptive control structure

Depending on how the adaptation is determined and depending on how the controller parameters change, the basic structure can take various forms. With the development of process computers and their abilities for fast calculus, it has increased in recent years the control systems with use of process computers for the industrial processes, taking over the functions of automatic controllers, adaptation devices or compensation devices from the systems.

1.2 . Stages of structural synthesis of automatic control systems

a) Preliminary analysis of the technological process In this stage we determine the input and output for the technological process, any state variables or intermediate signals which can be measured and determine the time evolution of the process. We then determine the command signal, the input-output channels, the imposed normal operating requirements and the operation safety. The process parameters variation limit and the limits for the measurable and command signal are determined, in order to choose the transducers and the execution elements.

b) Choosing the control system structure Structure is chosen according to the following factors:

- automated process configuration, the nature and variation of measurable outputs, the control variables, measurable and immeasurable disturbances and their variation character; - imposed qualitative performance under dynamic and stationary regime; - estimated cost for the control system (design, equipment, installation and commissioning), the degree of damping and available funds; - equipment available for the operation safety required by the process to ensure practical realization conditions.

c) Choosing the elements connecting the control device to the process Transducers are chosen according to the following factors: compliance with the safety and operating requirements of the process (danger of explosion, precision, sensitivity) and mounting conditions. Pneumatic or electronic transducers are chosen with the degree of protection required by the mounting place; the measurement range of the transducer has to be 10-15% higher than the variation range of measured variables during normal working conditions; specifying the required adapters in case the variation range of the transducer output signal differs from the command device measurable range (IU converters, IP, analog-digital converters); where there are large distances between the transducer and the command device intermediate power amplifiers are inserted (distance transmission) if the transmitter cant compensate for line losses; if the transducers has a nonlinear static characteristics (generally given by the sensing elements, such as diaphragms, nozzles, thermocouples, RTD, etc..) and the transducer does not ensure linearity, linearization additional elements are inserted in series with the transducer (radical extractors, power, compensation elements). In the case of digital systems we analyze the advantages of digital or analog linearization. The transfer function of the transducer and the ancillary items must correspond to an aperiodic first order element:

The time constant must satisfy the relationship 10TT <Td, where Td is the dominant time constant characterizing the process. The transfer factor KT is determined by the ratio:

where yT is the variation range of the output signal of the transducer (8mA or 16mA for unified electronic system and 0.8bar for pneumatic system) and ui is the measurement range of the transducer (ui = (1.1 - 1.15). yprocess). Execution elements provides the link between the control device and the plant, allowing the conversion and power amplification for the controller output variation in variations of command variables for the technological plant. In most cases, in continuous processes, input signals chosen as control signals are flow fluids and in this case the execution elements will be composed of a pneumatic actuator piston or membrane, controlled with unified pneumatic signal (0.2 - 1bar ) and a control valve driven by an actuator. In these cases, if the controller is electronic (analog or digital), between the control and the actuator device we intercalate a pressure-current converter that will be incorporated into the implementation of the execution element for the analysis under dynamic regime. The ensemble transfer function, named execution element (converter I/P, actuator, control valve) can be treated as first order aperiodic element in the case of diaphragm actuator or simple effect piston, and as an integrator for double acting piston actuator:

where TE is considered much smaller than the dominant time constant of the process, and KE is calculated as the ratio of the execution element output variation range and the variation range of the controller output.

d) Determining the technological plant transfer function Technological plants can be considered as a multivariable complex nonlinear systems, and the mathematical model describing the behavior of input - state - output that results based on general laws of conservation of mass, energy and momentum, is generally a system of nonlinear differential equations. If the job of an automated control system is to ensure a steady-state operating mode for the technological plant, then the dynamic behavior superimposed on the steady-state behavior (assuming small variations of the variables from

the stationary regime) is described by a system of linear differential equations. In this case, applying the principle of superposition for the equivalent dynamic system corresponding to variables variations we can determine the transfer functions for the the command - output channel or the disturbance-output channel. There are times when we cant develop a mathematical model using the analytical methods because some dependency coefficients that appear in the state equations are not known. In other situations we obtain complex transfer functions that cant be used in the controller structure design or for the control law. In these cases typical test signals are used, usually step signals and approximate the studied channels by simplified transfer functions of I or II order with or without time delay (the tangent method is presented in figures 5 and 6).

Fig. 5. First order process with time delay

Fig. 6. Approximating higher order processes

If a better approximation for the end of the transient response is desired then we can decrease the time delay up to 0.8*. Another method for approximating the transfer function is the Cohen-Coon method, presented in figure 7. Noting with ys the final value at which the response stabilizes to the step input, we determine the time at which the values of 0.28*ys and 0.632*ys are reached and marke them with t28 and t632 respectively. We then calculate the constants:

The parameters is beeing used in the tuning Cohen-Coon criteria.

Fig. 7. Cohen-Coon method

e) Controller parameters In general for the control loops is preferred to have a PID control law with parameters generally tuned according to criteria that minimize the mean squared error. The conventional control transfer function is chosen according to the following relationship, where the interdependence factor is = 2 for electronic controllers, and = 1 for pneumatic controllers. The parasitic time constant T 0.1*TD results from the physical realizability of the derivative component.

In the case of a numeric controller, if one prefers a PID control law he will use the previous relationship with = 0 and = 0.1*TD. f) Tuning parameters calculation for processes with time delay The calculation formulas are presented in tables 1 and 2: Table 1. Optimal prescribed variable response

Table 2. Optimal disturbance response

g) Cotroller tuning for system in operation If the process allows us to bring the closed loop control system at the stability limit, or near it, then we bring the system controller at the P variant and progressively increase KR until obtaining a maintained oscillating regime. We note the amplification factor value for which this regime has been reached as KRlim and with Tlim the obtained oscillations period. The Ziegler-Nichols performance criterion establishes the relations for calculating the optimal tuning parameters.

If the system cant be brought to the stability limit, the experiment starts similar to the previous case but stops increasing KR when the transient response to the step signal has a reduction of oscillation amplitudes in the ratio 4:1. In this case KRoptim = 0.6..KRo, TI = 0.17*TO, TD = 0.06*TO where TO is the obtained oscillations period. BIBLIOGRAPHY 1. Matei Vntoru, Eugen Iancu, Camelia Maican,Gabriela Cnureci, Conducerea automat a proceselor industriale, Ed. Universitaria, Craiova, 2007. 2. Mihail Abrudean, Teoria sistemelor i control automat, Ed. Mediamira, 1998.