59,556 research outputs found
Computational burden reduction in Min-Max MPC
Minâmax model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced minâmax problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper
Min-Max MPC based on a computationally efficient upper bound of the worst case cost
Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10â12, 1987, pp. 1021â1026] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound can be computed with O(n3) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even in non-mathematical oriented programming languages such as those found in industrial embedded control hardware. A simulation example is given in the paper
Non-linear predictive control for manufacturing and robotic applications
The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems
Robust predictive feedback control for constrained systems
A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model
Minâmax MPC using a tractable QP problem
Minâmax model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the minâmax problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the minâmax problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
Predictive Second Order Sliding Control of Constrained Linear Systems with Application to Automotive Control Systems
This paper presents a new predictive second order sliding controller (PSSC)
formulation for setpoint tracking of constrained linear systems. The PSSC
scheme is developed by combining the concepts of model predictive control (MPC)
and second order discrete sliding mode control. In order to guarantee the
feasibility of the PSSC during setpoint changes, a virtual reference variable
is added to the PSSC cost function to calculate the closest admissible set
point. The states of the system are then driven asymptotically to this
admissible setpoint by the control action of the PSSC. The performance of the
proposed PSSC is evaluated for an advanced automotive engine case study, where
a high fidelity physics-based model of a reactivity controlled compression
ignition (RCCI) engine is utilized to serve as the virtual test-bed for the
simulations. Considering the hard physical constraints on the RCCI engine
states and control inputs, simultaneous tracking of engine load and optimal
combustion phasing is a challenging objective to achieve. The simulation
results of testing the proposed PSSC on the high fidelity RCCI model show that
the developed predictive controller is able to track desired engine load and
combustion phasing setpoints, with minimum steady state error, and no
overshoot. Moreover, the simulation results confirm the robust tracking
performance of the PSSC during transient operations, in the presence of engine
cyclic variability.Comment: 6 pages, 5 figures, 2018 American Control Conferance (ACC), June
27-29, 2018, Milwaukee, WI, USA. [Accepted in Jan. 2018
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