James B. Rawlings Research Group


Jenny Wang
B.S. Ch.E., Rice University, 1996
Ph.D., University of Wisconsin-Madison, 2002
ywang[AT]bevo[DOT]che[DOT]wisc[DOT]edu

Current Work

Model Predictive Control (MPC) is a control theory that computes appropriate input control actions by optimizing a performance objective subject to a process model. The success of the control actions generally depends on the accuracy of the process model in spite of the feedback. Because process identification is difficult at best, process modelling errors occur frequently. Robust MPC is an MPC theory that increases the effectiveness of the control actions when modelling errors are present by explicitly accounting for the modelling errors in the controller design procedure.

Many robust control theories have been developed. Among linear control theories, H infinity robust control has perhaps become the most widely known during the last 15 years. Robust versions of MPC have also been developed and studied during the last 10 years. Campo and Morari (1987) studied minimizing, with respect to control moves, the maximum of the future deviations of the predicted output for the worst impulse response model subject to input and output constraints. Kothare et al. (1996) proposed minimizing, with respect to control law Kx, the "worst" infinite horizon performance objective subject to process models and input and output constraints. The gain was found by solving a linear matrix inequality. Michalska and Mayne (1993) replaced the terminal equality constraint for the prediction horizon of the model predictive controller with a terminal inequality constraint. Robustness was achieved by requiring the largest possible terminal state to lie within an invariant set. Lee and Cooley (1997) proposed the min-max predictive control strategy. The objective is to minimize the maximum cost, which is defined by the infinite horizon quadratic objective function, for all possible models in the uncertainty description subject to input constraints. Genceli and Nikolaou (1995) developed sufficient conditions for the robust stability and performance of nonlinear model predictive control systems. The systems are characterized by second order Volterra models with parametric uncertainty in the time domain. The systems are robustly stabilized by an end condition which states that the value of the process input at the end of the finite prediction horizon must be equal to the steady-state input value corresponding to the setpoint and the steady-state disturbance estimates. Zheng (1998) developed conditions that show a model predictive controller is robustly stable on a linear plant if and only if there exists a nominally stable model predictive controller for the linear plant. Badgwell (1996,1997) proposed a robustness constraint that requires the cost function values for every model in the uncertainty set either to remain constant or decrease at each time step, relative to the cost values computed using the current measured state and the restriction of the input. Nicolao et al. (1998) proposed the monotonicity-based robustness feature of the single model stabilizing receding horizon control, which guarantees that the cost function decreases monotonically at each time step. All of these approaches are based on state-space models with state feedback and measurement.

The robust MPC theory we are proposing uses a family $\Pi$ of output feedback models to compute input control actions that minimize the largest performance objective based on all possible time varying combinations of the time invariant models in $\Pi$ subject to input and output constraints. For this robust MPC theory to be feasible, there must exist an output feedback control law $K$ that stabilizes all model $(A_i,B_i) \in \Pi$. This robust MPC theory has the following properties:

  1. The controller uses output rather than state feedback.
  2. The controller stabilizes all models in $\Pi$.
  3. The controller can achieve offset free control by integrating the setpoint tracking error.

Publications

1
Yiyang Jenny Wang and James B. Rawlings.
A new robust model predictive control method. I: Theory and computation.
J. Proc. Cont., 14:231-247, 2004.

2
Yiyang Wang and James B. Rawlings.
A new robust model predictive control method. II: Examples.
J. Proc. Cont., 14:249-262, 2004.

3
Yiyang Wang.
Robust Model Predictive Control.
PhD thesis, University of Wisconsin-Madison, January 2002.

Personal Web Page: jbrwww.che.wisc.edu/~ywang

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University of Wisconsin
Department of Chemical Engineering
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