Process Identification And Pid Control Pdf
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- PID controller
- Advanced Methods of PID Controller Tuning for Specified Performance
- Neural PID Control Strategy for Networked Process Control
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A proportional—integral—derivative controller PID controller or three-term controller is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control.
In practical terms it automatically applies an accurate and responsive correction to a control function. An everyday example is the cruise control on a car, where ascending a hill would lower speed if only constant engine power were applied. The controller's PID algorithm restores the measured speed to the desired speed with minimal delay and overshoot by increasing the power output of the engine. The first theoretical analysis and practical application was in the field of automatic steering systems for ships, developed from the early s onwards.
It was then used for automatic process control in the manufacturing industry, where it was widely implemented in pneumatic, and then electronic, controllers. Today the PID concept is used universally in applications requiring accurate and optimized automatic control.
The distinguishing feature of the PID controller is the ability to use the three control terms of proportional, integral and derivative influence on the controller output to apply accurate and optimal control. The block diagram on the right shows the principles of how these terms are generated and applied.
Tuning — The balance of these effects is achieved by loop tuning to produce the optimal control function. The tuning constants are shown below as "K" and must be derived for each control application, as they depend on the response characteristics of the complete loop external to the controller. These are dependent on the behavior of the measuring sensor, the final control element such as a control valve , any control signal delays and the process itself.
Approximate values of constants can usually be initially entered knowing the type of application, but they are normally refined, or tuned, by "bumping" the process in practice by introducing a setpoint change and observing the system response. Control action — The mathematical model and practical loop above both use a direct control action for all the terms, which means an increasing positive error results in an increasing positive control output correction. The system is called reverse acting if it is necessary to apply negative corrective action.
Some process control schemes and final control elements require this reverse action. Although a PID controller has three control terms, some applications need only one or two terms to provide appropriate control. This is achieved by setting the unused parameters to zero and is called a PI, PD, P or I controller in the absence of the other control actions.
PI controllers are fairly common in applications where derivative action would be sensitive to measurement noise, but the integral term is often needed for the system to reach its target value.
Situations may occur where there are excessive delays: the measurement of the process value is delayed, or the control action does not apply quickly enough. In these cases lead—lag compensation is required to be effective. The response of the controller can be described in terms of its responsiveness to an error, the degree to which the system overshoots a setpoint, and the degree of any system oscillation. But the PID controller is broadly applicable since it relies only on the response of the measured process variable, not on knowledge or a model of the underlying process.
Continuous control, before PID controllers were fully understood and implemented, has one of its origins in the centrifugal governor , which uses rotating weights to control a process. This had been invented by Christiaan Huygens in the 17th century to regulate the gap between millstones in windmills depending on the speed of rotation, and thereby compensate for the variable speed of grain feed. This was based on the millstone-gap control concept.
Rotating-governor speed control, however, was still variable under conditions of varying load, where the shortcoming of what is now known as proportional control alone was evident. The error between the desired speed and the actual speed would increase with increasing load.
In the 19th century, the theoretical basis for the operation of governors was first described by James Clerk Maxwell in in his now-famous paper On Governors. He explored the mathematical basis for control stability, and progressed a good way towards a solution, but made an appeal for mathematicians to examine the problem. About this time, the invention of the Whitehead torpedo posed a control problem that required accurate control of the running depth. Use of a depth pressure sensor alone proved inadequate, and a pendulum that measured the fore and aft pitch of the torpedo was combined with depth measurement to become the pendulum-and-hydrostat control.
Pressure control provided only a proportional control that, if the control gain was too high, would become unstable and go into overshoot with considerable instability of depth-holding. Another early example of a PID-type controller was developed by Elmer Sperry in for ship steering, though his work was intuitive rather than mathematically-based.
It was not until , however, that a formal control law for what we now call PID or three-term control was first developed using theoretical analysis, by Russian American engineer Nicolas Minorsky.
He noted the helmsman steered the ship based not only on the current course error but also on past error, as well as the current rate of change;  this was then given a mathematical treatment by Minorsky. While proportional control provided stability against small disturbances, it was insufficient for dealing with a steady disturbance, notably a stiff gale due to steady-state error , which required adding the integral term. Finally, the derivative term was added to improve stability and control.
Trials were carried out on the USS New Mexico , with the controllers controlling the angular velocity not the angle of the rudder. The Navy ultimately did not adopt the system due to resistance by personnel. Similar work was carried out and published by several others in the s. The wide use of feedback controllers did not become feasible until the development of wideband high-gain amplifiers to use the concept of negative feedback.
This had been developed in telephone engineering electronics by Harold Black in the late s, but not published until This dramatically increased the linear range of operation of the nozzle and flapper amplifier, and integral control could also be added by the use of a precision bleed valve and a bellows generating the integral term.
The result was the "Stabilog" controller which gave both proportional and integral functions using feedback bellows. From about onwards, the use of wideband pneumatic controllers increased rapidly in a variety of control applications. Air pressure was used for generating the controller output, and also for powering process modulating devices such as diaphragm-operated control valves. They were simple low maintenance devices that operated well in harsh industrial environments and did not present explosion risks in hazardous locations.
They were the industry standard for many decades until the advent of discrete electronic controllers and distributed control systems. In the s, when high gain electronic amplifiers became cheap and reliable, electronic PID controllers became popular, and the pneumatic standard was emulated by mA and 4—20 mA current loop signals the latter became the industry standard.
Pneumatic field actuators are still widely used because of the advantages of pneumatic energy for control valves in process plant environments. Most modern PID controls in industry are implemented as computer software in distributed control systems DCS , programmable logic controllers PLCs , or discrete compact controllers.
Electronic analog PID control loops were often found within more complex electronic systems, for example, the head positioning of a disk drive , the power conditioning of a power supply , or even the movement-detection circuit of a modern seismometer.
Discrete electronic analog controllers have been largely replaced by digital controllers using microcontrollers or FPGAs to implement PID algorithms. However, discrete analog PID controllers are still used in niche applications requiring high-bandwidth and low-noise performance, such as laser-diode controllers. Consider a robotic arm  that can be moved and positioned by a control loop.
An electric motor may lift or lower the arm, depending on forward or reverse power applied, but power cannot be a simple function of position because of the inertial mass of the arm, forces due to gravity, external forces on the arm such as a load to lift or work to be done on an external object. By measuring the position PV , and subtracting it from the setpoint SP , the error e is found, and from it the controller calculates how much electric current to supply to the motor MV.
The obvious method is proportional control: the motor current is set in proportion to the existing error. However, this method fails if, for instance, the arm has to lift different weights: a greater weight needs a greater force applied for the same error on the down side, but a smaller force if the error is on the upside.
That's where the integral and derivative terms play their part. An integral term increases action in relation not only to the error but also the time for which it has persisted. So, if the applied force is not enough to bring the error to zero, this force will be increased as time passes.
A pure "I" controller could bring the error to zero, but it would be both slow reacting at the start because the action would be small at the beginning, needing time to get significant and brutal the action increases as long as the error is positive, even if the error has started to approach zero. A derivative term does not consider the error meaning it cannot bring it to zero: a pure D controller cannot bring the system to its setpoint , but the rate of change of error, trying to bring this rate to zero.
It aims at flattening the error trajectory into a horizontal line, damping the force applied, and so reduces overshoot error on the other side because of too great applied force. Applying too much impetus when the error is small and decreasing will lead to overshoot.
After overshooting, if the controller were to apply a large correction in the opposite direction and repeatedly overshoot the desired position, the output would oscillate around the setpoint in either a constant, growing, or decaying sinusoid. If the amplitude of the oscillations increases with time, the system is unstable. If they decrease, the system is stable.
If the oscillations remain at a constant magnitude, the system is marginally stable. In the interest of achieving a controlled arrival at the desired position SP in a timely and accurate way, the controlled system needs to be critically damped. A well-tuned position control system will also apply the necessary currents to the controlled motor so that the arm pushes and pulls as necessary to resist external forces trying to move it away from the required position.
The setpoint itself may be generated by an external system, such as a PLC or other computer system, so that it continuously varies depending on the work that the robotic arm is expected to do. A well-tuned PID control system will enable the arm to meet these changing requirements to the best of its capabilities.
Variables that affect the process other than the MV are known as disturbances. Generally, controllers are used to reject disturbances and to implement setpoint changes. A change in load on the arm constitutes a disturbance to the robot arm control process.
In theory, a controller can be used to control any process that has a measurable output PV , a known ideal value for that output SP , and an input to the process MV that will affect the relevant PV. Controllers are used in industry to regulate temperature , pressure , force , feed rate ,  flow rate , chemical composition component concentrations , weight , position , speed , and practically every other variable for which a measurement exists.
The PID control scheme is named after its three correcting terms, whose sum constitutes the manipulated variable MV. The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Equivalently, the transfer function in the Laplace domain of the PID controller is. The proportional term produces an output value that is proportional to the current error value.
The proportional response can be adjusted by multiplying the error by a constant K p , called the proportional gain constant. A high proportional gain results in a large change in the output for a given change in the error.
If the proportional gain is too high, the system can become unstable see the section on loop tuning. In contrast, a small gain results in a small output response to a large input error, and a less responsive or less sensitive controller.
If the proportional gain is too low, the control action may be too small when responding to system disturbances. Tuning theory and industrial practice indicate that the proportional term should contribute the bulk of the output change.
The steady-state error is the difference between the desired final output and the actual one. SSE may be mitigated by adding a compensating bias term to the setpoint AND output or corrected dynamically by adding an integral term.
The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. The integral in a PID controller is the sum of the instantaneous error over time and gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain K i and added to the controller output. The integral term accelerates the movement of the process towards setpoint and eliminates the residual steady-state error that occurs with a pure proportional controller.
However, since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the setpoint value see the section on loop tuning. The derivative of the process error is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain K d.
The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, K d.
Advanced Methods of PID Controller Tuning for Specified Performance
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A new method with a two-layer hierarchy is presented based on a neural proportional-integral-derivative PID iterative learning method over the communication network for the closed-loop automatic tuning of a PID controller. It can enhance the performance of the well-known simple PID feedback control loop in the local field when real networked process control applied to systems with uncertain factors, such as external disturbance or randomly delayed measurements. The proposed PID iterative learning method is implemented by backpropagation neural networks whose weights are updated via minimizing tracking error entropy of closed-loop systems. The convergence in the mean square sense is analysed for closed-loop networked control systems. To demonstrate the potential applications of the proposed strategies, a pressure-tank experiment is provided to show the usefulness and effectiveness of the proposed design method in network process control systems. Networked control systems NCSs make it convenient to control large distributed systems. Process control can integrate the controlled process and the communication network of computational devices, but sensors and actuators cannot be directly used in a conventional way because there are some inherent issues in NCS, such as delay, packet loss, quantization, and synchronization.
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Neural PID Control Strategy for Networked Process Control
We propose a new and simple on-line process identification method for the automatic tuning of the PID controller. It does not require a special type of test signal generators such as relay or P controller only if the signals are persistently exciting. That is, a user can choose arbitrary signal generators such as relay, a P controller, the controller itself, pulse signal and step signal generator because it needs only the measured process output and the controller output.