Adaptive feedback/feedforward PID controller

Details Adaptive feedback/feedforward PID controller Adaptive feedback/feedforward PID controller

2000-06-20

2003-06-10

Follansbee, John A. (Department: 2121)

Data processing: generic control systems or specific application

Generic control system, apparatus or process

Optimization or adaptive control

C700S028000, C700S031000, C700S052000, C318S561000, C318S610000

Reexamination Certificate

active

06577908

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to process control techniques and, more particularly, to an adaptive PID (Proportional, Integral and Derivative) controller that is characterized by parameter values derived from an interpolation of process model parameters.
2. Description of the Related Art
Logic-based, controller-switching strategies have been proposed as a potential approach to the implementation of adaptive process control. See, for example, Morse, F. M. Pait, and S. R. Weller, “Logic-Based Switching Strategies for Self-Adjusting Control, 33
rd
IEEE Conference on Decision and Control
(December 1994). In general, logic-based controller-switching strategies may be categorized into one of two approaches.
The first approach is predicated on prerouted controller tuning. In principle, prerouted tuning involves sequential evaluation of candidate controllers that are drawn from a prescribed set. The evaluation is complete when a controller is identified that performs satisfactorily. Prerouted tuners are relatively simple to design and impose few requirements on controller structure. However, the advantages of prerouted tuners are overshadowed by intrinsically poor performance with respect to tuning time. That is, an inordinate length of time is often required to select the optimal controller from the prescribed set.
An alternative approach is based on an identifier-based, parameterized controller that consists of two parameter-dependent subsystems, an identifier, the primary function of which is to generate an output estimation error, and an internal controller. The control signal that is fed back to the process is based on a current estimate of the process model. In general, the estimates of the process model are selected from a suitably defined model set. The overall strategy is based on the concept of “cyclic switching.” Cyclic switching can be employed with or without process excitation. A worthwhile review and evaluation of this approach to process control adaptation is given by K. S. Narendra and J. Balakrishnan in “Adaptive Control Using Multiple Models,”
IEEE Transactions on Automatic Control
, Vol. 42, No. 2, pp. 177-187 (February 1997). That article discloses an architecture with N identification models operating in parallel. Corresponding to each model is a parameterized controller. At any point in time, one of the models is selected by a switching rule, and the corresponding control input is used to control the process. Models may be fixed or adaptive. The rationale for using fixed models is to ensure that there exists at least one model characterized by parameters sufficiently close to those of the unknown process. The approach yields the desired speed of adaptation, but requires that a significant number of models be constructed. In addition, because fixed models are capable of precisely representing only a finite number of environments, adaptive models must be used to asymptotically improve accuracy.
The practical application of switching strategies poses a number of problems, largely due to the number of models required for a reasonable process approximation. Even in a simple single-input, single-output (SISO) system, a self-tuner can reasonably be expected to necessitate hundreds of fixed models in order to achieve satisfactory performance. The requirement for numerous process models exacerbates exponentially in multivariable systems. More effective solutions require consideration of the specific process model structure and controller type, and suggest the replacement of a simple switching strategy with more elaborate procedures.
A significantly modified approach has been offered by Gendron for a Dahlin controller. See, S. Gendron, “Improving the Robustness of Dead-Time Compensators for Plants with Unknown of Varying Delay,”
Control Systems
90
Conference
(Helsinki 1990). Gendron therein describes a simple first-order-plus-dead-time process model, according to which process adaptation is effected exclusively through dead time variation. Rather than relying on simple switching, the controller assumes a process model that is derived a weighted sum of models that are characterized by disparate dead times. Each model in the set generates a prediction of the process output, and the corresponding weight is adjusted automatically as a simple function of the prediction error. The concept has been extended to incorporate into a Dahlin controller both process gain and dead time uncertainty in the Dahlin controller construct.
In general, there exist two prominent approaches for designing a PID adaptive controller. To wit: the direct approach, and the indirect, or identifier-based, approach. As has been indicated above, because the identifier-based approach is advantageous for switching strategies, the subject invention generally pursues this approach for the design of an adaptive switching PID controller. Because there appears to be no art related to the switching of PID controllers, the present invention is deemed most nearly related to the classical identifier-based, adaptive PID controller. The result is an adaptive PID controller, coupled with a Recursive Least Squares (RLS) estimator, that tracks changes in the model parameters. Typical problems associated with recursive identifiers are known to include the selection of initial parameters, insufficient excitation, filtering, parameters wind-up, and sluggish parameter tracking speed. It is known that performance improvements may be obtained by simplifying the process model. A worthwhile example of this solution is given by Astrom and Hagglund in “Industrial Adaptive Controllers Based on Frequency Response Techniques,”
Automatica
, Vol. 27, No. 4, pp. 599-609 (1991). The controller described therein is designed to perform adaptation in the frequency domain, and performs tuning in response to setpoint changes and natural disturbances. A specific tuning frequency is selected by applying band-pass filters to the process input and output. The frequency of the filters is set by the auto-tuner (tuner-on-demand). The auto-tuner defines the ultimate period using a relay oscillation technique, prior to adaptive tuner operation. The adaptive tuner defines the process gain for the tuning frequency using a simplified RLS estimator. The tuner has the capability to easily track changes in a process gain. However, when a change in a dead time or in a time constant is encountered, the point tracked no longer exhibits a −&pgr; phase, and controller tuning becomes inaccurate. It is known that tuning can be improved significantly by applying several tuning frequencies and by using an interpolator to define a frequency with phase −&pgr;. Alternatively, it is possible to instantly operate with only one tuning frequency and adjust that frequency after each tuning cycle to track a phase −&pgr;. Both designs accommodate subsequent set point changes and natural disturbances and may inject external excitations at the controller output or at the setpoint input. Although such tuners do not exhibit the constraints of the previous technique, they are significantly more complex.
A more serious detriment of both designs is the reliance on a relatively primitive adaptive model that recognizes only two parameters: Ultimate Gain and Ultimate Period. A tuner model of this design is suitable for Ziegler-Nichols tuning or some cognate modifications, but will not satisfy the requirements of many applications where Internal Model Control (IMC) or Lambda tuning are preferred. A simple RLS identifier may be used to determine static gain for the feedforward control. However, that approach does not provide the process feedforward dynamics required for adequate feedforward control. In addition, because feedforward signals are load disturbances, and perturbation signals can not be injected as they may into the feedback path, the approach suffers the problem of insufficient excitations.
A more sophisticated solution to feedforward adaptation is disclosed in U.S. Pat. No. 5,043,863, “Multivariable Adap

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