Minimal prototype controllers

The basic idea is to specify the desired response of the system to a specific type of disturbance and then, knowing the model of the process, back-calculate the controller required. There is no guarantee that the minimal-prototype controller will be physically realizable for the given process and the specified response. Therefore, the specified response may have to be modified to make the controller realizable. 

Now the minimal-prototype controller for step changes in setpoint is... 

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. 

With these specifications for JffJ and Jf, we can calculate the minimal-prototype controller for ramp setpoint changes using Eq. (20.15). 

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... 

This controller is physically realizable. Therefore minimal-prototype control should be attainable. But what about intersample rippling Let us check the manipulated variable. 

As our final minimal-prototype controller, let us consider the Dahlin algorithm. The basic notion is to specify a desired step setpoint response that looks like a deadtime followed by an exponential rise up to the setpoint. See Fig. 20.4. 

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. 

Now, for this first-order process, Eq. (15.53) gives HGAf(,). Plugging this into Eq. (15.57) gives the minimal-prototype controller. 

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 ... 

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. 

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

An alternative to discrete PI or PID algorithms is one that is determined by sampled-data techniques using the z-transformation. This algorithm does not have parameters K Tr, and td, but is expressed as a ratio of polynomials in powers of Z whose coefficients are specified to achieve a certain response. Some criteria for selecting coefficients are like the methods described in the previous section while others select the coefficients to obtain a specified type of closed-loop response. For example, Dahlin s method specifies the response to a step change in set point to be a first-order lag with dead time. The minimal prototype sampled-data algorithm is a type of optimal control in which the output is specified to reach set point, that is, zero error, in the fastest time without exlubiting oscillations. 

In the United States, regulation of emissions from new automotive vehicles has followed the prototype-replicate route. The argument for routine annual automobile inspection is that cars should be regularly inspected for safety (brakes, lights, steering, and tires) and that the additional time and cost required to check the car s emission control system during the same inspection will be minimal. Such an inspection certainly pinpoints cars whose emission control system has been removed, altered, damaged, or deteriorated and force such defects to be remedied. The question is whether... 

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