Step 7. Try an optimal design. If the trial-and-error compensators do not give entirely satisfactory performance, consider a design based on optimal control. The symmetric root locus will show possible root locations from which to select locations for the control poles that meet the response specifications; you can select locations for the estimator poles that represent a compromise between sensor and process noise. Plot the corresponding and its robustness to parameter changes. You can modify the pole locations until a best compromise results. Returning to the symmetric root locus with different cost measures is often a part of this step. or computations via the direct functions Iqr and Iqe can be used. Another variation on optimal control is la propose a find structure controller with unknown parameters. formulate a performance cost function. and use parameter optimization to find a good set of parameter values.
Compare the optimal design yielding the most satisfactory frequency response with the transform-method design you derived in Step 5. Select the better of the two before proceeding to Step 8.
Step 8 Build a computer model, and compute (simulate) the performance of the design. After reaching the best compromise among process modification, actuator and sensor selection, and controller design choice, run a computer, run a computer model of the system. This model should include important nonlinearities such as actuator saturation, realistic noise sources, and parameter variations you expect to find during operation of the system. The simulation will often identify sensitivities that may lead to going back to Step 5 or even Step 2. Design iterations should continue until the simulation confirms acceptable stability and robustness. As part of this simulation you canoften include parameter optimization, in which the computer tunes the free parameters far best for best performance. In the early stages of design, the model you simulate will be relatively simple; as the design progresses, you will study more complete and detailed models. At this step it is also possible to compute a digital equivalent of the analog controller. Some refinement of the controller parameters may be required to account for the effects of digitization. This allows the final design to be implemented with digital processor logic.
If the results of the simulation prove the design satisfactory, go to Step 9; otherwise return to Step 1.
Step 9. Build a prototype. As the final test before production, it is common to build and test a prototype- At this point you verify the quality of the model, discover unsuspected vibration and other modes, and consider ways to improve the design. Implement the controller using an embedded software/hardware. Tune the controller if necessary. After these tests, you may want to reconsider the sensor, actuator, and process and return to Step 1-unless time, money, or ideas have run out.
This outline is an approximation of good practice; other engineers will have variations on these themes. In some cases you may wish to carry out them in a different order, to omit a step, or to add one. The stages of simulation prototype construction vary widely, depending on the nature of the system. For systems where a prototype is difficult to test and rework (for example, a satellite) or where a failure is dangerous (for example, active stabilization of a high-speed centrifuge or landing a human on the moon), most of the design verification is done through simulation of some sort. It may take the form of a digital numerical simulation, a laboratory-scale model, or a full-size laboratory model with a simulated (for example, feedback control for an automotive fuel the simulation step is often skipped entirety; design verification and refinement are accomplished by working with prototype.
One of the issues raised above (Step 6) was the important consideration for changing the plant itself. In many cases, proper plant modifications can provide additional damping or increase in stiffness, change in mode shapes, reduction of system response to disturbances, reduction of Coulomb friction, and change in thermal capacity or conductivity, and so on. It is worth elaborating on this byway of specific examples from the authors' experiences. In a semiconductor processing example, the edge ring holding the wafer was identified as a limiting factor in closed- loop control. Modifying the thickness of the edge ring and using a different coating material reduced the heat losses and, together with relocating one of the temperature sensors closer to the edge ring. resulted in significant improvement in control performance. In another application, thin film processing, simply change the order of the two incoming flows resulted in significant improvement in uniformity of the film. In an application on vapor deposition using RF plasma, the shape of the target was modified lo be curved to counter the geometry effects of the chamber and yielded substantial improvements in deposition uniformity.
