Ultimate Limits to Performance

Whether You Are Talking About Advanced PID Control or Model-Predictive Control, the Final Control Element Determine How Well You Can Achieve Your Control Objectives

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Greg McMillan and Stan Weiner bring their wits and more than 66 years of process control experience to bear on your questions, comments and problems. Write to them at controltalk@putman.net.

McMillan & WeinerBy Greg McMillan and Stan Weiner

Stan: Sometimes we get so caught up in sophisticated control strategies and control system technologies that we forget the ultimate limits to what we can achieve. Whether you are talking about advanced PID control or model-predictive control, the dead time, noise, speed and resolution-sensitivity of measurement and the final control element determine how well you can achieve your control objectives.

In this column, we are going to talk about some of these ultimate limits. We are grouping resolution with sensitivity, which set, respectively, the quantization and threshold for detection, communication and actuation. For speed, we are focusing on the rate of change of the process and the sample rate of the control system. 

Greg: Dead time is the deadliest of the limitations. Without dead time, I would be out of a job. During the loop dead time, the controller does not see or does not affect the process. The ultimate limit for peak error for rise time is proportional to the loop dead time. The ultimate limit for integrated error is proportional to the dead time squared. The sources of dead time are insidious. The measurement and final control element sensitivity divided by the signal rate of change and one half of a sample or scan time are additional sources of deadtime not commonly recognized. The phase shift and ultimate period are proportionally increased. Sensitivity and sample time are particularly important in silicon wafer/circuit  manufacturing. nTrolus Inc. (http://ntrolus.com/Default.aspx) is a leader in model-based control for semiconductor production and green energy systems. We talked to its president, Mark Ekblad, who understands the significance of these limits.

Stan: What are manufacturers predominantly controlling in semiconductor production?

Mark: Most of the applications involve temperature control. In general, we can only turn off heat. There are no brakes. We have only ambient cooling or sometimes a fixed static cooling load provided by cooling jackets. Consequently, the speed of temperature change for heating and cooling is drastically different.

The process often has a near-integrating response where the temperature essentially ramps. Setpoint overshoot must be minimized because of the sensitivity of the process and the long settling time. The aggressive performance of the PID with conventional Ziegler-Nichols tuning relying on feedback action leads to quality problems. Fuzzy logic and gain scheduling is sometimes used, but the special tuning requirements complicate the implementation.

Greg: Bioreactor temperature control has similar requirements and problems, particularly in single-use bioreactors with disposable liners, bench-top and pilot plant units, and the small production-scale units that have only heaters. Large bioreactors have jackets with temperature-water systems that can provide a cooling rate commensurate with the heating rate. Even here, the tuning for no overshoot is not easy. The dynamic reset limit PID option is essential to prevent the integral action of the primary temperature loop from changing the setpoint of the secondary loop or the final control element too quickly. (See my February 18 blog post, “Dynamic Reset Limit, www.modelingandcontrol.com/2011/02/dynamic_reset_limit.html)

Stan: What are the final control elements that are used in the semiconductor industry?

Mark: The temperature controllers are typically manipulating power to a heater. Pulse-width modulation is used to vary the amount of on time in a cycle. The typical power controllers used today and their performance values from the least to the most expensive are shown in Table 1.

The electromechanical contacts are only suitable for very slow systems with very loose control requirements. Solid-state relays offer tighter control, but are not fast enough for many wafer temperature control systems used in silicon wafer processing. Silicon control rectifiers (SCR) offer the fastest and most reliable control with the longest life. The phase-fired SCR commands true power regardless of line voltage or heater resistance. It also offers the tightest control, but filtering must be employed to reduce EMI noise.

Greg: What are some of the faster rates of temperature transitions?

Mark: The temperature of semiconductor wafers goes from room temperature to 1150 °C. The ramp rate might be 100 °C/min. Yet customers think they can use a 1-sec controller cycle time that corresponds to a 1.6 °C error. For rapid thermal processing, the ramp rate could be 200 °C/sec. A sample rate of 100 Hz is then needed. Faster-than-required sample rates cause unnecessary wear of contactors and relays, and reduce the signal-to-noise ratio because the true change in the process temperature becomes a smaller percentage of the noise from the process, EMI and resolution limits.

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