Constrained Receding Horizon Predictive Control Research Articles

Mejora de la estabilidad, robustez y tiempo de cómputo en CRHPC con BDU

In this work, different control laws of Model Predictive Control (MPC) are offered in order to improve the stability and robustness aspects. The CRHPC (Constrained Receding-Horizon Predictive Control) provides de stability (in the absence of uncertainty), and the BDU (Bounded Data Uncertainties) technique provides a guided regularization improving the robustness and ill-conditioning, presenting the original CRHPC-BDU. The objective of this work consists, on the one hand, of offering alternative control laws of the CRHPC, using different mathematical tools and comparing them. These ones constitute the basis for the different statements for extending these strategies to the CRHPC-BDU. So, one of the main contribution consists of obtaining a more robust and with less computationalcost version of CRHPC-BDU.

Robust constrained receding-horizon predictive control via bounded data uncertainties

The main objective of this work consists of obtaining a new robust and stable Model Predictive Control (MPC). One widely used technique for improving robustness in MPC consists of the Min–Max optimization, where an analogy can be established with the Bounded Data Uncertainties (BDU) method. The BDU is a regularization technique for least-squares problems by taking into account the uncertainty bounds. So BDU both improves robustness in MPC and offers a guided way of tuning the empirically tuned penalization parameter for the control effort in MPC due to the duality that the parameter coincides with the regularization one in BDU. On the other hand, the stability objective is achieved by the use of terminal constraints, in particular the Constrained Receding-Horizon Predictive Control (CRHPC) algorithm, so the original CRHPC–BDU controller is stated, which presents a better performance from the point of view of robustness and stability than a standard MPC.

Robust and stable predictive control with bounded uncertainties

Min–Max optimization is often used for improving robustness in Model Predictive Control (MPC). An analogy to this optimization could be the BDU (Bounded Data Uncertainties) method, which is a regularization technique for least-squares problems that takes into account the uncertainty bounds. Stability of MPC can be achieved by using terminal constraints, such as in the CRHPC (Constrained Receding-Horizon Predictive Control) algorithm. By combining both BDU and CRHPC methods, a robust and stable MPC is obtained, which is the aim of this work. BDU also offers a guided method of tuning the empirically tuned penalization parameter for the control effort in MPC.

Polynomial Approach to Constrained Receding Horizon Predictive Control

This contribution addresses an alternative stability proof of the Constrained Receding Horizon Predictive Control (CRHPC) problem based on the closed-loop design.The second aim of this paper is to show that the actual horizon lengths are too conservative. A modified method that zeroes only the tracking error while relaxing the assumption about future control increments is derived. Again, the stability proof is performed directly in closed-loop and not as usually, in open-loop.Finally, it is shown how to rewrite the proposed controller within the predictive control framework.

Experimental verification of stabilising predictive control

This paper presents the results of testing one type of stabilising predictive control, constrained receding horizon predictive control (CRHPC), obtained during real-time experiments on laboratory-scale devices and on an industrial plant. The performance of CRHPC is compared with that of the conventional generalised predictive control (GPC) and PID. The control algorithms are implemented in an adaptive mode with a recursive estimator. The results show that the CRHPC is more sensitive to the process time delay and uncertainties compared with the conventional GPC.

Multivariable Predictive Control

Abstract This paper presents some real-time laboratory experiments with a multivariable predictive control law based on the Generalized Predictive Control (GPC) and Constrained Receding Horizon Predictive Control (CRHPC) to demonstrate their performance under various conditions. The proposed controllers rests upon a set of MISO models of multivariable system. The control signal is generated subject to amplitude and increment constraints.

Constrained Predictive Control for Motor Drives

Generalized predictive control (G.P.C.) is an efficient strategy for machine tools applications. However, high performance may require the consideration of constraints on the system. This paper presents a modified version of G.P.C, called C.R.H.P.C. (Constrained Receding Horizon Predictive Control), which imposes constraints on the final output values, so that the output matches the reference over a further constraint range. An important result is that theorems guarantee stable closed loop behaviour for particular sets of tuning parameters. This method applied to the velocity control of a motor drive proves that an effective definition of constraints enables better results for severe conditions of use.

Application of Constrained Receding Horizon Predictive Control to a Benchmark Problem

A polynomial RST controller designed by using the constrained receding horizon predictive control (CRHPC) method is presented for the control of a system with flexible transmission and variable load. The main difference from GPC consists in imposing constraints on the final output values and ensuring stability for a particular set of tuning parameters. The robustness of this controller, elaborated for a medium load case, is tested in different load configurations, looking at frequency features (phase and gain margins, sensitivity functions) and step response behaviours (including disturbance rejection).

Stabilising properties of constrained predictive control

Standard generalised predictive control (GPC) and constrained receding-horizon predictive control (CRHPC) stability results have traditionally been derived in the state-space, using the properties of the solution of the Riccati equation associated with the control law. Unfortunately this type of study does not readily extend to constrained control laws which are nonlinear. By invoking the monotonicity, with respect to time, of the receding-horizon cost function, however, an extension of the stability properties of a subclass of GPC, termed GPC/sup infinity /, and of CRHPC may be obtained, when inequality constraints are added to the control objective. The problem of feasibility (i.e. the compatibility of the constraints) is also becoming a major area of interest in predictive control. In GPC/sup infinity / and CRHPC, the feasibility problem is compounded by the use of end-point equality constraints on the tracking error. A new concept called setpoint conditioning is introduced here, which may be used to resolve the incompatibilities between the inequality and the end-point equality constraints, without compromising stability.

Numerical robustness and efficiency of generalised predictive control algorithms with guaranteed stability

Three recent publications proposed modifications to the generalised predictive control algorithm which guarantee closed-loop stability. Of these the first two adopt the same philosophy, namely that of constrained receding horizon predictive control (CRHPC), whereas the third adopts a stable generalised predictive control (SGPC) strategy by first stabilising then controlling the plant. The purpose of the paper is to examine the relationship between CRHPC and SGPC. It is shown that, theoretically, the two approaches are equivalent, but is is also shown that CRHPC could be subject to significant numerical instability problems. Two alternative improved implementations of CRHPC are proposed, but SGPC is shown to have the advantage in terms of numerical stability and computational efficiency.

Receding-horizon predictive control with exponential weighting

Exponential weighting of future tracking errors and control increments is employed for receding-horizon predictive control and seen to improve the dynamic behaviour of the closed-loop system. A sufficient condition for the asymptotic stability of generalized predictive control (GPC) with these weightings is derived. The condition can be easily satisfied whereas the corresponding condition for GPC with constant weighting is highly restrictive. In the case of constrained receding-horizon predictive control (CRHPC), a prescribed degree of stability is obtained just as with infinite-horizon optimal control using the same type of weighting. This makes it possible to use a simplified CRHPC law with no weighting on the tracking error but which guarantees convergence to the set-point faster than a bounding exponential

Constrained receding-horizon predictive control

Constrained receding-horizon predictive control (CRHPC) is intended for demanding control applications where conventional predictive control designs can fail. The idea behind CRHPC is to optimise a quadratic function over a ‘costing horizon’ subject to the condition that the output matches the reference value over a further constraint range. Theorems show that the method stabilises general linear plants (e.g. unstable, nonminimum-phase, dead-time). Simulation studies demonstrate good behaviour with even nearly unobservable systems (where generalised predictive control is ineffective) and that control-costing is a particularly effective tuning parameter.