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For this example, create a 2-output, 3-input system. For instance, examine the dimensions of mag. Similarly, phase 1,3,10 contains the phase of the same response. Identify parametric and nonparametric models based on data. Create a Bode plot that includes both systems. Identify a transfer function model based on data. Obtain the standard deviation data for the magnitude and phase of the frequency response.
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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 which required accurate control of the running depth.
Use of a depth pressure sensor alone proved inadequate, and a pendulum which 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 which, if the control gain was too high, would become unstable and go into overshoot, with considerable instability of depth-holding.
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 angle of the rudder.
Similar work was carried out and published by several others in the s. Industrial control[ edit ] Proportional control using nozzle and flapper high gain amplifier and negative feedback The wide use of feedback controllers did not become feasible until the development of wide band 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. Compressed air was used both for generating the controller output, and for powering the process modulating device, such as a diaphragm-operated control valve.
They were simple low maintenance devices which operated well in a harsh industrial environment, and did not present an explosion risk 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 4—20 mA current loop signals were used which emulated the pneumatic standard. However field actuators still widely use the pneumatic standard because of the advantages of pneumatic motive power for control valves in process plant environments.
Showing the evolution of analogue control loop signalling from the pneumatic to the electronic eras. Current loops used for sensing and control signals.
A modern electronic "smart" valve positioner is shown, which will incorporate its own PID controller. 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 analogue controllers[ edit ] 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 analogue 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. 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.
The sensed position is the process variable PV. The desired position is called the setpoint SP.
The difference between the PV and SP is the error e , which quantifies whether the arm is too low or too high and by how much. The input to the process the electric current in the motor is the output from the PID controller.
It is called either the manipulated variable MV or the control variable CV. 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. Proportional[ edit ] The obvious method is proportional control: the motor current is set in proportion to the existing error.