By Peter Nachtwey
Delta Computer Systems Inc.
Vancouver, Wash.

Thousands of different hydraulic motion control applications exist, and you must choose the optimum control algorithm to get the best performance out of each motion axis. Sometimes a combination of control methods is required. This article explores some of the more common algorithms that are supported by commercially-available hydraulic motion controllers. We will focus on hydraulic positioning, and just touch on pneumatic and pressure control.

Open-loop control
A surprising number of applications use open-loop control. These include cases where the cylinder must move to unknown hard stop positions in order to align or measure objects such as logs in a sawmill. In such applications — where position and velocity control are not critical — open-loop control is often preferred over closed loop control. With open-loop control, the motion controller is not working actively to match the actual position, velocity, or pressure to computed target values. Therefore, it does not track the error between the actual and target values. Because error does not build up, the cylinder will not move abruptly forward should the load be reduced suddenly. Open-loop control is often combined with closed-loop control, with each used in different parts of the machine cycle where it is best suited. For example, open loop can be used in the retract direction to quickly open a press so a part can be ejected. Tuning is simplified because only the extend (pressing) direction must be tuned — the open-loop portion does not.

Closed-loop control
Applications requiring profile following; synchronization; gearing; a high degree of flexibility, accuracy, and speed; or the ability to maintain precision with changing loads must use closedloop control, which comes in many flavors.

Some simple analog controllers operate with just proportional control, where the drive signal changes as a function of the magnitude of the difference between actual and target position or pressure. Proportional control, P, by itself will suffice on some hydraulic systems if enough mechanical friction exists to provide damping. However, many hydraulic systems tend to be under-damped (like a mass on a spring) so adding only P gain tends to make any oscillations worse. And because a P-gain-only controller must have error to get the required output to move at the desired speed, a lot of following error occurs, and the following error increases with velocity. Other gain terms are required for tighter control, and each plays a different part.

The integrator gain, I, often is necessary to get an axis to move into position quickly and reliably. Again, a proportional-only control system needs to have an error in order to generate a non-zero output. In an ideal world, even a little output would move the cylinder to its set point. However, the mechanical realities of a system — such as changes in the null characteristics of a valve, or friction between the moving parts — may keep the cylinder from getting to the target set point. The integrator component of the control equation integrates error over time, eventually causing the output to increase or "wind up" to whatever value is necessary to cause the cylinder to move.

The derivative (also referred to as differential) gain, D, provides electronic damping that helps keep the cylinder from oscillating as the proportional gain is increased. Ideally, increasing the derivative gain will tend to damp, or even eliminate, the oscillations. How well the derivative terms work depends on a few important factors, such as feedback resolution and maintaining known sampling times. Because the derivative gain is multiplied by the error in velocity, velocities must be measured and calculated accurately.

Although the three gains of the PID seem to be independent of each other, mathematical relationships exist between the PID gains that must be maintained to achieve a critically damped or over-damped response that does not overshoot the set point.

Feed forwards are the key
Using the P, I, and D terms together in a control algorithm is helpful in improving the response of a machine. However, a limitation to using PID-based controls alone is that no output will be generated to drive the valve unless an error is present. In many applications this is not a problem, but precise tracking actually requires estimating the required output before the error occurs. That's where feed forwards play a role. Unlike PID gains, which are multiplied by the feedback error, feed forward gains are predictive and multiplied by the target velocity and acceleration, then summed together to generate a contribution to the output.

The concept is really very simple. Precisely tuned hydraulic systems require separate gains to achieve the desired velocity and acceleration in each direction of motion. As the motion controller moves the target position from one point to another, it also generates a target velocity and acceleration. These values are then multiplied by their respective feed forward gains to generate the required move at the current velocity and acceleration.

In theory, no error should exist if the predictive elements are computed correctly. However, real systems are seldom exactly linear, and the loads on many systems change from cycle to cycle. This causes errors that the PID can correct. In general you should be able to predict the required output within 5% of the desired goal using feed forwards, so the PID component of the closed-loop control algorithm only needs to correct the last 5%. This is much better than forcing the PID gains to do all the work.

Because the controller multiplies the instantaneous velocity and acceleration by the feed forward gains to determine the feed forward contribution to the output, these values should change smoothly without discontinuity. Otherwise, the control output will change in steps. Ideally, motion profiles with simple linear ramps, Figure 1(a), should only use velocity feed forwards because acceleration changes in steps. (Physical systems cannot make step changes in acceleration anyway, and attempts to do so will cause following errors.) To take full advantage acceleration feed forwards, S-curves or some other acceleration limiting technique must be used, Figure 1(b). Feed forwards should be used whenever axes must be tightly synchronized, or when precise gearing or profile tracking is needed, including applications such as flying cutoff saws and flying shears

I-PD: Another form of PID
Sometimes the target position is not generated by the motion controller. Instead, it may be generated by a joystick or the outer loop of another PID, or some other external source, Figure 1(c). The target position in these cases is not guaranteed to move smoothly from one point to the next. A PID control algorithm will try to follow a "noisy" target, resulting in "noisy" cylinder motion. The target position or the error can be filtered to smooth the output to the cylinder. Another technique is to use a form of PID called the I-PD. This form of PID uses the error only for calculating the integrator term. The P and D terms use only the negative feedback from the actual position. Because the P and D terms do not depend on the error between the target position and actual position, the controller will not generate large changes in the control output in response to noisy target signals or when step changes in the target position occur, Figures 1(c) and 1(d). Another way of describing the result in terms familiar to control system experts is to say that a well tuned I-PD system effectively turns the controller, cylinder, and load into a multiple-pole low pass filter.

Of course, not following the target position precisely when using filers or the I-PD algorithm limits the precision of profile tracking or synchronization. So while the I-PD is not suitable for every application, it should be considered when the target positions, velocities, or accelerations are not smooth.

Active damping
Active damping includes several methods of using feedback and a controller to electronically remove unwanted motion or oscillations. Active damping is normally required on systems that have a low natural frequency (they can be modeled as a mass on the end of a spring) and a high static-to-dynamic friction ratio. In these applications the force builds up across the piston until the static friction force is overcome and the piston starts to move. When the piston moves, the force across the piston falls below the dynamic friction force and the piston stops.

Any system that suffers from this stiction, or chatter, when running in open-loop mode will also do the same in closed loop mode. Borderline systems also tend to exhibit the same stiction action when in closed loop mode. The solution is to limit the acceleration, or the rate-ofchange of the force on the piston.

This is problematic because calculating the instantaneous acceleration from position transducers is usually not feasible. Instead, some method of obtaining acceleration feedback is needed. The most direct way to do this is to attach an accelerometer to the carriage or cylinder that is moving the load, but this can put the accelerometer in a nasty environment.

Alternatively, the differential force across the piston can be used to estimate the acceleration. This requires a controller with the necessary analog inputs to connect to the two pressure sensors and the ability to calculate the differential force on-the-fly. This technique is not as accurate as the accelerometer approach but is commonly used and very effective at solving stiction or chattering problems. Figure 2 contains the motion plot of an actively damped system running an I-PD control algorithm.

Active damping reduces the rate of force buildup across the piston and works best when the objective is to get from one point to another as smoothly as possible. Of course, active damping also limits the maximum acceleration and deceleration, which, in turn, limits the ability to follow a motion profile. If this is the primary objective, then a larger bore cylinder should be considered.

Another method of setting up an active damping control algorithm is to use a model based control system that can internally estimate accurate accelerations. The advantage is that no extra hardware is required. The disadvantage is that the system must be relatively linear so that an accurate model can be developed. This is why non-linear valve spools and pneumatic systems are difficult to model.

For best performance, it is better to design a hydraulic motion axis to have a high natural frequency and a linear response. But when extremely large masses must be positioned, at some point the extra expense of making the system hydraulically "stiff" becomes too great, so the system must be damped electronically.

Pressure/force control
Because fluid power is so well suited for applying force, we must briefly mention pressure/force control. Today, pressure/force control, P/F, and dual-loop position-pressure/force control, P-P/F, algorithms are often used. Other systems may only need closed loop for P/F and use open loop for position. In some pressure applications, position PIDs can be used for pressure/force control. Other applications may need special features for combining open loop position and single loop P/F PID.

Dual-loop P-P/F algorithms offer more flexibility than singleloop algorithms. Because a controller cannot simultaneously fully control position and pressure, two PIDs are used — a position PID and a P/F PID, referred to together as a P-P/F PID. Both PIDs must be tuned and some method (such as a pressure threshold) used to transfer between the modes, so only one PID is operating at a time.

For many applications, a pressure limit mode is the best solution, Figure 3. In this case, both PIDs run simultaneously, and the minimum output is used. Much can be discussed about P-P/F control and future articles will cover this topic in more depth.

Machine designers need to know that one size doesn't fit all in terms of hydraulic motion control. Many control algorithms are used in hydraulic applications, and the right one to use depends on the control needs of the application, Table 1. Some applications can benefit from combining two or three of the control algorithms discussed, depending on what part of the machine cycle is running. Discussing your application with the motion controller manufacturer early in the design process will help ensure that the controller has the algorithms you need.

Figure 1. Simple trapezoidal motion profiles allow the use of PID algorithms and velocity feed forwards, 1(a), but abrupt edges limit the use of acceleration feed forwards. Adding S-curves to the trapezoidal motion profiles allows the full use of acceleration feed forwards in the control algorithm, 1(b). This waveform produces smoother motion and does not provoke oscillations. Filtering or I-PD algorithms should be used if a motion controller must work with target signals that are noisy or contain step changes, 1(c) and 1(d), such as those from a joystick or other external source.

Figure 2. Typical example of an actively damped system.

Figure 3. Plot of a system where velocity is being controlled during a move operation until a pressure limit is reached.

Table 1. Table summarizing the types of algorithms required for optimum performance in specific applications.

For more information, visit www.deltamotion.com or contact the author at peter@deltamotion.com.