As shown in: http://www.ecircuitcenter.com/Circuits/pid1/pid1.htm.
How could a PID controller convert the voltage error to current?
Take the control of AC-DC-AC converter as an example, where inner loop current control and outer loop voltage ( DC link voltage ) control are used. The voltage error, which comes from the outer loop, can be converted to a current reference using a PID controller. The current reference is used for the inner loop control.
However, as shown in: http://en.wikipedia.org/wiki/File:VectorSensorlesssBD.jpg, the current loop is the outer loop, and the voltage loop is the inner loop. So how could a PID controller convert the current error to voltage (or voltage reference)?
Probably your question is about apparent dimensional inconsistency. The way this question is posed is sometimes confusing. For example in a PID controller we directly add the error (difference between the reference and actual plant output), its integral and its derivative all together and say that this represents another quantity with a unique dimension! A closer look reveals that we are dealing effectively with representative dimensionless quantities, the instantaneous MAGNITUDE of which is reflected by a voltage (usually) in analog or by a number in digital realization of the controller. This change in dimension of a measured variable (say speed) to this dimensionless representation is done by the sensor which we use for feedback. If a PID controller works on an input 'u' to produce an output 'y', then we can add the P, I & D outputs because the respective constants have the dimensions: kp (dimensionless), ki (time) and kd (1/time). The final output is suitably scaled for synthesizing the plant control input and this step is where the controller output (dimensionless) is multiplied by an appropriate base value to render the correct physical dimension. For example, when a VSI is used to drive a motor, the controller outputs a modulation signal (dimensionless) and compares it to a carrier signal (dimensionless) of suitable amplitude, to generate a binary pulse-train (dimensionless), which is multiplied by the inverter constant (dc bus voltage or some fraction of it) to synthesize the voltage input to the motor.
Depending on your exact requirements, you can possibly do all of this with a simple resistor! (voltage drop across a resistor is proportional to current through it; current through is proportional to voltage across!). If you just want to measure current, for example, put a 1 ohm resistor in series; the voltage drop will be equal to the current flow (V = IR).
More generally, if you need some degree of isolation between input and output (i.e. to avoid any loading effects), you could use a transimpedance (sometimes termed transresistance) or transconductance amplifier. TIAs can be built from standard voltage op-amps. The classical inverting voltage amplifier configuration is really a transimpedance amplifier: a circuit which provides an output voltage that is proportional to an input current (the inverting voltage amplifier function is provided by sinking the input current through an input resistor connected to a virtual pseudo-ground).
See here:
http://en.wikipedia.org/wiki/Transimpedance_amplifier
To go the other way, you can use a transconductance amplifier, which is electrically a bit different from your standard differential voltage amplifier.
http://en.wikipedia.org/wiki/Operational_transconductance_amplifier
The output of a PID controller (or even PI controller) is never converted to a pre-defined quantity and depends on what is done with it in the following stage. This is because the integral function creates a time varying output even if the input is constant. The output must be used logically to create a closed loop control.
In your first example, the voltage is compared to check the state of charge of the dc capacitor for proper operation, and if it is low, the input current must be increased to compensate charge. Thus voltage error is converted to input current reference in your loop structure.
In your second example, lower velocity (or speed) implies torque must be increased which is through increase in torque producing component of stator current. Since stator current is controlled by stator voltage, the desired current is converted to desired voltage through the use of the motor model (not shown separately in your referred figure) such that the desired voltage can be applied to motor through the PWM inverter. However, note that there is no voltage feedback loop, since any error created will reflect back as speed error, to be taken care by the speed controller again.
Thanks, Sujit.
Yes there is no voltage loop here, instead it's the speed loop. Thank you for correcting that out.
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