【正文】 eve adequate control performance. A problem with the Derivative term is that small amounts of measurement or process noise can cause large amounts of change in the output. It is often helpful to filter the measurements with a lowpass filter in order to remove higherfrequency noise ponents. However, lowpass filtering and derivative control can cancel each other out, so reducing noise by instrumentation means is a much better choice. Alternatively, the differential band can be turned off in many systems with little loss of control. This is equivalent to using the PID controller as a PI controller. 6. Cascade control One distinctive advantage of PID controllers is that two PID controllers can be used together to yield better dynamic performance. This is called cascaded PID control. In cascade control there are two PIDs arranged with one PID controlling the set point of another. A PID controller acts as outer loop controller, which controls the primary physical parameter, such as fluid level or velocity. The other controller acts as inner loop controller, which reads the output of outer loop controller as set point, usually controlling a more rapid changing parameter, flowrate or accelleration. It can be mathematically proved that the working frequency of the controller is increased and the time constant of the object is reduced by using cascaded PID controller.[vague] 7. Physical implementation of PID control In the early history of automatic process control the PID controller was implemented as a mechanical device. These mechanical controllers used a lever, spring and a mass and were often energized by pressed air. These pneumatic controllers were once the industry 12 analog controllers can be made from a solidstate or tube amplifier, a capacitor and a resistance. Electronic analog PID control loops were often found within more plex electronic systems, for example, the head positioning of a disk drive, the power conditioning of a power supply, or even the movementdetection circuit of a modern seismometer. Nowadays, electronic controllers have largely been replaced by digital controllers implemented with microcontrollers or FPGAs. Most modern PID controllers in industry are implemented in software in programmable logic controllers (PLCs) or as a panelmounted digital controller. Software implementations have the advantages that they are relatively cheap and are flexible with respect to the implementation of the PID algorithm. nomenclature and PID forms Pseudocode Here is a simple software loop that implements the PID algorithm: Ideal versus standard PID form The form of the PID controller most often encountered in industry, and the one most relevant to tuning algorithms is the standard form. In this form the Kp gain is applied to the Iout, and Dout terms, yielding: Where Ti is the Integral Time previous_error = 0 start: error = setpoint actual_position P = Kp * error I = I + Ki * error * dt D = (Kd / dt) * (error previous_error) output = P + I + D previous_error = error wait(dt) goto start 13 Td is the Derivative Time In the ideal parallel form, shown in the Controller Theory section the gain parameters are related to the parameters of the standard form through and Kd = KpTd. This parallel form, where the parameters are treated as simple gains, is the most general and flexible form. However, it is also the form where the parameters have the least physical interpretation and is generally reserved for theoretical treatment of the PID controller. The standard form, despite being slightly more plex mathematically, is more mon in industry. form of the PID controller Sometimes it is useful to write the PID regulator in Laplace transform form: Having the PID controller written in Laplace form and having the transfer function of the controlled system, makes it easy to determine the closedloop transfer function of the system. / interacting form Another representation of the PID controller is the series, or interacting form. This form essentially consists of a PD and PI controller in series, and it made early (analog) controllers easier to build. When the controllers later became digital, many kept using the interacting form. [edit] References Liptak, Bela (1995). Instrument Engineers39。 the Proportional, the Integral and Derivative values. The Proportional value determines the reaction to the current error, the Integral determines the reaction based on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing. The weightedsum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating tuning the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability. Some applications may require using only one or two modes to provide the appropriate system control. This is achieved by setting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are particularly mon, since derivative action is very sensitive to measurement noise, and the absence of an integral value may prevent the system from reaching its target value due to the control action. 2 A block diagram of a PID controller Note: Due to the diversity of the field of cont