Minimal-Prototype Design

One of the most interesting and unique approaches to the design of sampled-data controllers is called minimal-prototype design. It is one of the earliest examples of model-based controllers. 

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Thus the system is critically damped as expected for minimal-prototype design. 

Minimal-prototype controllers are designed for a specific type of input. A controller that is designed for a step change will perform quite differently if the change actually has some other shape. The following example illustrates the point. 

Load inputs can also be designed for using minimal-prototype methods. For load disturbances only, Eq. (20.13) gives... 

We want to design a minimal-prototype controller for a unit step setpoint change. The output is supposed to come up to the new setpoint in one sampling period. Substituting Eq. (20.47) into Eq. (20.20) gives... 

Design a sampled-data minimal-prototype digital compensator for step changes in setpoint that does not ripple. 

Design a minimal prototype sampled-data controller for the pressurized tank... 

Design a minimal-prototype sampled-data controller for a first-order system with a deadtime that is three sampling periods. The input is a unit step change in setpoint. 20.6. Design minimal prototype controllers for step changes in setpoint and load for a process that is a pure integrator. 

Finally, it should be noted that many existing digital controller design techniques (Kuo (55)) yield an optimal or "perfect11 control in deadbeat or minimal prototype controller designs, the exact form of the response is pre-specified, rather than minimizing the integral of the squared error. 

Design a minimal prototype algorithm using the following specifications (1) unit step load change and (2) the output should return to zero at the fifth sampling instant and remain at zero for every sampling instant after the fifth. 

Design minimal-prototype controllers for step changes in setpoint and load for a process that is a pure integrator. 

Design a minimal-prototype controller for a unit step change in load such that the maximum change in the manipulated variable M cannot exceed some specified maximum value Afmax ... 

Many different types of models may be produced to aid product development, test theories, experiment with solutions, etc. However, when the design is complete, prototype models representative in all their physical and functional characteristics to the production models may need to be produced. When building prototypes, the same materials, locations, subcontractors, tooling, and processes should be used as will be used in actual production so as to minimize the variation (see also clause 4.4.8.3). 

The problem of permeability exists whenever a plastic material is exposed to vapor, moisture, or liquids. Typical cases are electrical batteries, instruments, components installed underground, encapsulated electrical components, food packaging, and various fluid-material containers. In these cases, a plastic material is called upon to form a barrier either to minimize loss of vapor or fluid or to prevent the entrance of vapor or fluid into a product. From the designers viewpoint, the tolerable amount of permeation established by test under conditions of usage with a prototype product of correct shape and material is the only direct answer. 

Derived from standard desktop printers, drop-on-demand techniques, such as electrohydrodynamic jet (e-jet) printing, solid freeform fabrication (SFF), or piezoelectric inkjet printing, are among a few notable examples of rapid prototyping techniques that have been developed to pattern biomaterials. With the incorporation of a user friendly computer interface, these techniques have been employed to process a number of multiplexed, biomaterial constructs without the use of masks, stamps, or any other time consuming processing equipment. The design of such constructs with minimal feature sizes in the microliter to picoliter resolution has been demonstrated and will be discussed below. 

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