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# Closed-loop speed control of hydraulic motors

A closed-loop speed control uses an amplifier driven by system error, which is the difference between the command (where we want the speed to be) and the feedback (where the speed actually is).

A closed-loop speed control is shown in simplified, schematic form in Figure 1. The amplifier, A, is a differential type, meaning that it subtracts the tachometer feedback signal from the command and generates the difference (the error signal), amplifies it, and provides a driver current to the valve coil. The amplifier is driven by the system error. Of course, the error is the difference between the command (where we want the speed to be) and the feedback (where the speed actually is). The amplifier could be analog, consisting of operational amplifiers, resistors, and capacitors, or it could be totally digital. Figure 1. This closed-loop speed control uses a tachometer to sense shaft speed and feed it back to a servo or proportional amplifier. Speed is set with the command signal, C.

The amplifier gain is the number of amperes of coil current, I, per volt of error signal. In the analog circuit, its value is adjusted in the application — probably by changing a potentiometer setting. In the digital case, the amplifier gain is set by entering it through a keyboard, or with a pointing device and setting a slider on a computer screen.

### A case in point

To understand how this system works, consider a basic example. Suppose that the tachometer constant is 1 V/1000 rpm, a convenient value that doesn't require rocket science to do some basic calculations. Next, suppose the command voltage is 3 V. So the question arises: What is the resulting shaft speed?

A hasty response might be 3000 rpm. However, a bit of logic tells us this cannot be. If the shaft speed is 3000 rpm, consider the paradox we have created: If the shaft speed is 3000 rpm, the tachometer feedback voltage must be 3 V. With a 3-V feedback, and 3-V command, the error must be zero. With an error of zero, there can be no current. If there is no current, the spool must be centered, so the motor must be stopped! Therefore, a speed of 3000 rpm produces a speed of 0 rpm, a totally absurd conclusion! It's necessary to look at the feedback control system in a less simplistic way.

### Reasoning inside the box Figure 2. The speed gain block is structured to have command voltage as input and motor speed as output.

To understand the function of the closed-loop control system, it is helpful to adopt the concept of speed gain, Figure 2. Speed gain refers to the rate at which the output speed of the motor increases with an increase in command signal input. Depending on how the system is analyzed, the units on speed gain could be output rpm /A of valve coil current. In another analysis, the units might be output rpm/V of input command voltage. The later will be used in the analysis that follows.

The choice of units dictates the equipment making up the black box that constitutes the so-called speed gain. That black box will eventually become a block in a closed-loop block diagram. So now, the outer limits are the input command voltage at one extreme and the shaft speed on the other. The question then arises, What is inside the box?

Clearly, the command voltage enters the servo or proportional amplifier, so command voltage must be the first element inside the box. The output of the amplifier, current, goes into the servo or proportional valve. The output of the valve powers the hydraulic motor, so the valve must be in the box. An obvious addition is the motor itself. Figure 3. The speed control gain block contains all the system elements except for the tachometer.

The suitability of two more components is more subtle: the power unit and the load. The power unit supplies constant pressure to the valve. However, if everything else remains fixed, an increase in supply pressure will cause more flow and, thus, cause the motor shaft speed to increase. Similarly, with everything else fixed, if the load increases, shaft speed decreases. Therefore, both of these elements must be included in the speed gain block. Comparing Figures 1 and 3 (the speed gain block) to the list of components (listed above in bold text) reveals that the speed gain block contains everything except the tachometer.

This exercise of reasoning out the contents of the speed gain block serves at least two instructional purposes. First, it collects the thoughts and gives a basis for calculating the gain of the block. Second, it forms the basis for conducting a series of tests for measuring the speed gain.

### Testing for control gain The gain can be calculated with the VCMM equation — an effort that is quite beneficial before assembling any hardware. However, the calculated value will make more sense if we assume the hardware exists, and we proceed to measure the speed gain. The speed gain block will be set up as in Figure 3. The system to be tested contains all the components that will produce output speed with and input voltage. This defines the physical limits of speed gain.

The test is set up, first, by mounting and plumbing all the hardware and wiring all the electronic parts accordingly. With hydraulic power applied, the supply pressure is set to the desired value. The test can be conducted using several different supply pressures. However, we will assume that just one pressure will be studied for our tentative setup.

Next, a method must be arranged so that the mechanical load on the motor shaft can be adjusted to each of several desired values. A common practice is to use a hydraulic pump as a load, and then use an adjustable load valve to vary its pressure — which behaves as a variable load torque on the shaft. A torque transducer is commonly used to ensure that the load is correctly set, and a tachometer measures the output shaft speed. So, in the end, we are going to use all of the hardware of the closed-loop system, but we will be testing without the loop closed. That is, the tachometer output signal will not be connected to the feedback input on the servo or proportional amplifier. Not surprisingly, this is referred to as an open-loop test.

The test is conducted with the supply pressure set to the desired value, the load is set to zero or near zero, then the command voltage is set to zero. The command voltage is then increased in convenient increments to a value that results in maximum desired motor speed. While the command signal is high, the load is increased, say, to 33% of maximum torque. Then the command signal is lowered in convenient increments to zero. Figure 4. Output speed of the motor is plotted against command voltage at three different load values and constant supply pressure. Speed gain is the slope of the curve at any one of the load values.

This process is repeated through the full range of load torques up to the desired maximum, and the command is varied at each load setting. Minimum recorded data consist of supply pressure, command voltage, load torque, and output speed. If the control valve has essentially linear flow metering characteristics (rectangular metering slots), the test data will look similar to that in Figure 4.

Speed gain is the slope of the curve at the operating load in the application. It is clear from the diagram that at no-load, Load 1, the speed gain is higher than when the load is high, Load 3. Intuitively, this make sense. The motor will tend to slow down as we increase the load torque. The green lines are straight line approximations to the slightly curved graphs of actual test data.

Now we can modify the definition of speed gain slightly. It is the slope of the speed versus input command curve under the condition of constant load torque. This means we must know the load torque in the application in order to correctly predict the speed gain of the system. Because loads can be complex — and load torque rarely is constant — we more often than not have to settle for an approximation, or some "average load torque," or perhaps, conduct analysis under the extremes of zero load and maximum load.