Mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix

This paper investigates mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix (MTRM). Based on the fact that system stability as well as its performance is dependent on MTRM, a mode feedback controller is proposed to perform control on MTRM such that system stability is achieved. Meanwhile, this strategy can help to improve system performance since it can adjust the occurrence probability of each subsystem. Firstly, taking into account that MTRM will totally determine system stability in absence of state feedback controller, the existence and restrictions on mode feedback controller are discussed where two cases are included. Then, based on a quadratic stabilization cost function that is a combination of state cost and control cost, a feasible solution of mode feedback control strategy is then obtained with its detailed algorithm given. Simulation results including comparisons with current state feedback mechanism are provided to illustrate the effectiveness of the proposed strategy.     

A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design

This article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that its robustness cannot be guaranteed because it consists of linear quadratic regulator (LQR) and Kalman observer, and due to observer incorporation within the LQR framework results in loss of robustness which is undesirable. Therefore, it is necessary to recover the robustness by tuning the controller which further plays havoc with system performance and control effort for certain plants. The present work addresses the investigation of the trade-off between multiobjective indexes (formulated on the basis of robustness, optimal control, and performances) through three multiobjective optimization algorithms as NSGA-II, multiobjective simulated annealing and multiobjective particle swarm optimization. The tuned parameters meet the competitive multiobjective performance indexes that are verified through simulation results. The Pareto front with multiple solutions helps to design a robust controller depending on the weightage given to the respective performance indexes. Simulation results reveal that the proposed multiobjective control strategy helps in recovering the characteristics of LQG/LTR.     

Two-degree-of-freedom controllers for multivariable model-matching systems: Application to a continuous stirred tank reactor (CSTR)

In this paper we study a robust control problem by the approach of model-matching design with a two-degree-of-freedom controller. First we give a parametrization of all stabilizing compensators from the viewpoint of independent design of feedforward and feedback controllers. Second, utilizing the modern Wiener-Hopf method, we solve the optimal robust control problem. The proposed controller can directly deal with the intrinsic problem of process interaction, plant uncertainty and controller saturation irrespective of whether the plant is stable or unstable. The design method is applied to a continuous stirred tank reactor (CSTR) system. Computer simulation shows results with satisfactory performance.     

A novel hybrid model predictive control design with application to a quadrotor helicopter

In this paper, a novel control design strategy based on a hybrid model predictive control in combination with fuzzy logic control is presented for a quadrotor helicopter system. In the proposed scheme, a 2‐part control structure is used. In the first part, a linear model predictive controller with receding horizon design strategy is combined with a nonlinear model predictive controller, which is applied as the main controller. In the second part, a 2‐level fuzzy logic controller is utilized to assist the first controller when the error exceeds a predefined value. The proposed nonlinear predictive control method utilizes a novel approach in which a prediction of the future outputs is used in the modeling stage. Using this simple technique, the problem can be solved using linear methods and, thereby, due to considerable reduction in the computational cost, it will be applicable for the systems with fast dynamics. Moreover, the fuzzy logic controller is used as a supervisor to adjust a proportional‐integral‐derivative controller to enhance the system performance by decreasing the tracking error. The proposed scheme is applied to a model of quadrotor system such that the difference between the predicted output of the system and the reference value is minimized while there are some constraints on inputs and outputs of the nonlinear quadrotor system. Simulation results demonstrate the efficiency of the proposed control scheme for the quadrotor system model.     

Cost function optimization for predictive control of a five-phase IM drive

Model predictive control has been used, for some time now, as a method to directly control power converters in electrical systems. The usual practice is tuning the cost function of the controller to obtain a certain compromise solution over the whole operating range of the system. This method is extended here to consider multiple, locally optimal, and tunings. The design objectives (tracking error, switching frequency, etc) are used to define a unique performance index that is locally optimized. In this way, the parameters of the cost function are linked to the current operating point. The tuning at each operating point is obtained numerically solving the optimization of the performance index. Although the idea can be applied to induction machines with any number of phases, in this paper, a five-phase induction motor is considered for presentation. This system is a demanding case due to the extra number of phases compared with the traditional three-phase motor. Simulation and experimental results are presented to assess the proposed predictive controller.     

Neural net control of nonlinear plants through state feedback

A heuristic design method for state feedback fixed (non‐adaptive) neural net controller in nonlinear plants is presented. The design method evolves as a natural extension of the optimal control strategies employed in linear systems. A multi‐layered feed‐forward neural network is used as the feedback controller. The controller is trained to directly minimize a suitable cost function comprised of the plant output, states and the input. The optimization is carried out using a gradient scheme that employs the recently developed concept of block partial derivatives. The applicability of the proposed design method is demonstrated through simulated examples. Simulation studies include a variety of optimal control problems in nonlinear plants such as: minimum energy and minimum fuel problems, state tracking, output servo with integrator, and unconstrained and constrained regulation. Copyright © 2000 John Wiley & Sons, Ltd.     

Energy-efficient cabin climate control of electric vehicles using linear time-varying model predictive control

A cabin climate control system, often referred to as a heating, ventilation, and air conditioning (HVAC) system, is one of the largest auxiliary loads of an electric vehicle (EV), and the real-time optimal control of HVAC brings a significant energy-saving potential. In this article, a linear-time-varying (LTV) model predictive control (MPC)-based approach is presented for energy-efficient cabin climate control of EVs. A modification is made to the cost function in the considered MPC problem to simplify the Hessian matrix in utilizing quadratic programming for real-time computation. A rigorous parametric study is conducted to determine optimal weighting factors that work robustly under various operating conditions. Then, the performance of the proposed LTV-MPC controller is compared against a rule-based (RB) controller and a nonlinear economic MPC (NEMPC) benchmark. Compared with the RB controller benchmark, the LTV-MPC reaches the target cabin temperature at least 69 s faster with 3.2% to 15% less HVAC system energy consumption, and the averaged cabin temperature difference is 0.7°C at most. Compared with the NEMPC, the LTV-MPC controller can achieve comparable performance in temperature regulation and energy consumption with fast computation time: the maximum differences in temperature and energy consumption are 0.4°C and 2.6%, respectively, and the computational time is reduced 72.4% on average with the LTV-MPC.     

Predictive control of a water distribution system based on process historian data

In this paper, a heuristic historian data-based predictive control strategy is presented and used to control a water distribution system simulated using the EPANET software, in particular, the Richmond water distribution system. The control actions are computed based on past historian data. The historian stores closed-loop operation data of the process with different controllers used in the past, which may not provide sufficient information for a precise system nor controller identification. The proposed predictive controller computes the current control actions as a weighted sum of past control actions so that an estimation of the performance cost over a prediction horizon is minimized. Only a subset of the past control actions in the historian close to the current state of the process is considered in the current control computations to carry out a local linearization. This predictive strategy is well suited to control applications of large and complex processes for which it is difficult to carry out identification experiments such as water distribution systems. In the application example, the trajectories of a set of relay controllers are used through the proposed approach to take into account pressure constraints and periodic references.     

Model‐free online tuning of controller parameters using a globalized local search algorithm

In an earlier work, the authors proposed a globalized bounded Nelder‐Mead algorithm with deterministic restarts and a linearly growing memory vector. It was shown that the algorithm was a favorable option for solving multimodal optimization problems like controller tuning because of the greater probability of finding the global minimum and lesser numerical cost. Therefore, the algorithm was successfully used for model‐based offline tuning of sliding mode controller parameters for a servo‐pneumatic position control application. However, such offline tuning requires a sufficiently adequate system model, which, in some applications, is difficult to attain. Moreover, it is not generally appreciated as an essential requirement for controller tuning by the end user like the industry. An improvement in performance of optimization algorithm for tuning is expected if it relies on measurements coming directly from an actual physical system and not just its mathematical model. Therefore, in this paper, we apply the aforementioned algorithm for model‐free online optimization of controller parameters. The application involves the programmatic control of a real‐time interface of a physical system by the algorithm for data flow and logical decisions for optimization. For comparison with the results of the model‐based offline tuning suggested in earlier work, the sliding mode controller parameters are tuned online for the same position control application. The experimental results reveal that the system performance with controller parameters tuned online using the algorithm compares favorably to the one with model‐based offline tuning especially at higher priority level for accuracy. The improvement in system performance amounts to 21%.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

An optimized fuzzy continuous sliding mode controller combined with an adaptive proportional-integral-derivative control for uncertain systems

This article discusses the design of a hybrid fuzzy variable structure control algorithm combined with genetic algorithm (GA) optimization technique to improve the adaptive proportional-integral-derivative (PID) continuous second-order sliding mode control approach (APID2SMC), recently published in our previous article in the literature. In this article, first, as an improved extension to APID2SMC published recently in the literature, an adaptive proportional-integral-derivative fuzzy sliding mode scheme (APIDFSMC) is presented in which a fuzzy logic controller is added. Second, a GA-based adaptive PID fuzzy sliding mode control approach (APIDFSMC-GA) is introduced to obtain the optimal control parameters of the fuzzy controller in APIDFSMC. The proposed control algorithms are derived based on Lyapunov stability criterion. Simulations results show that the proposed approaches provide robustness for trajectory tracking performance under the occurrence of uncertainties. These simulation results, compared with the results of conventional sliding mode controller, APID2SMC, and standalone classical PID controller, indicate that the proposed control methods yield superior and favorable tracking control performance over the other conventional controllers.     

Reference output tracking control for a flexible air‐breathing hypersonic vehicle via output feedback

This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal output tracker using a time-weighted performance index

In this paper we develop necessary conditions for the optimality of discrete system feedback controllers using a performance index imposed of (1) time weighting of the states, (2) steady-state error weighting and (3) weighting of the control gain. The controller performance is demonstrated using an F-14 digital pitch rate controller. © 1998 John Wiley & Sons, Ltd.     

Adaptive fuzzy finite-time optimal control for switched nonlinear systems

This article addresses the adaptive fuzzy finite-time control problem for a class of switched nonlinear systems whose powers are positive odd rational numbers and vary with the switching signal. The fuzzy logic systems (FLSs) are used to approximate the unknown nonlinearities of the controlled systems, and then by combining backstepping control algorithm with adding a power integrator technique, an adaptive finite-time controller is designed. By modifying and optimizing the relevant design parameters of the proposed adaptive finite-time controller, a novel adaptive finite-time optimal control approach is developed. The proposed two adaptive finite-time optimal control schemes can guarantee semi-globally practically finite-time stability of the closed-loop system. Moreover, the adaptive finite-time optimal controller can also achieve optimized performance in relation to the cost functional. Finally, a simulation example is given to illustrate the effectiveness of the proposed two adaptive finite-time control strategies.     

A discrete-time optimal adaptive control law for a robot arm

The equations of motion describing a robot's dynamics are coupled and non-linear, making the design of an optimum controller difficult using classical techniques. In this work an explicit adaptive control law is proposed based on a discrete linear model for each link and on the minimization of a quadratic performance criterion for position error and total control effort. The system parameters are recursively estimated at each control step by use of least squares, with a typical sample time of 0.02 s. A computer simulation of the resulting scheme is performed to evaluate the controller. The simulation model, based on the first three links of an existing robot, includes detailed motor dynamics and treats the wrist assembly as a load mass. Simulated test paths requiring movement of the outer two links indicate that the controller adapts and that its behaviour is stable and convergent.     

Globalized and bounded Nelder‐Mead algorithm with deterministic restarts for tuning controller parameters: Method and application

This paper develops and examines an optimization algorithm for simulation‐based tuning of controller parameters. The proposed algorithm globalizes the Guin augmented variant of Nelder–Mead's nonlinear downhill simplex by deterministic restarts, linearly growing memory vector, and moving initial simplex. First, the effectiveness of the algorithm is tested using 10 complex and multimodal optimization benchmarks. The algorithm achieves global minima of all benchmarks and compares favorably against the evolutionary, swarm, and other globalized local‐search multimodal optimization algorithms in probability of finding global minimum and numerical cost. Next, the proposed algorithm is applied for tuning sliding mode controller parameters for a servo pneumatic position control application. The experimental results reveal that the system with sliding mode controller parameters tuned using the proposed algorithm targeting smooth position control with maximum possible accuracy, performs as desired and eliminates the need of manual online tuning for desired performance. The results are also compared with the performance of the same servo pneumatic system with parameters tuned using manual online tuning in an earlier published work. The system with controller parameters tuned using the proposed algorithm shows improvement in accuracy by 28.9% in sinusoidal and 42.2% in multiple step polynomials tracking.     

Optimal digital redesign of cascaded analogue controllers

This paper presents a new, optimal digital redesign technique for finding an optimal cascaded digital controller from the given continuous-time counterpart by minimizing a quadratic performance index. The control gains can be obtained by solving a set of Lyapunov equations. The developed optimal cascaded digital controller enables the state and/or outputs of the digitally controlled closed-loop sampled-data system to optimally match those of the original continuous-time closed-loop system at any instant between sampling periods. The developed control law can be implemented using inexpensive and reliable digital electronics with a relatively long sampling period.     

A state space self-tuning controller with integral action

The paper is concerned with the problem of designing a state space self-tuning controller with integral action for a class of unknown linear stochastic systems. The observer form of the innovations model of the system is used along with a single-stage quadratic-in-state-and-control performance index which includes a cross-weighting between system states and inputs. This results in a proportional estimated state plus integral output (P + I) controller in an incremental form. While it is analogous to the LQG-theory-based optimal adaptive controller in structure, computational simplification is achieved by the choice of a single-stage performance index and a direct estimation of the state estimator gain matrix. The new controller has the advantages of being applicable to both single-input/single output (SISO) and multi-input/multi-output (MIMO) minimum phase and non-minimum phase systems. The results are illustrated numerically through two simulation examples.     

Inverse optimal controller based on extended Kalman filter for discrete‐time nonlinear systems

In this study, we present an inverse optimal control approach based on extended Kalman filter (EKF) algorithm to solve the optimal control problem of discrete‐time affine nonlinear systems. The main aim of inverse optimal control is to circumvent the tedious task of solving the Hamilton‐Jacobi‐Bellman equation that results from the classical solution of a nonlinear optimal control problem. Here, the inverse optimal controller is based on defining an appropriate quadratic control Lyapunov function (CLF) where the parameters of this candidate CLF were estimated by adopting the EKF equations. The root mean square error of the system states is used as the observed error in the case of classical EKF algorithm application, whereas, here, the EKF tries to eliminate the same root mean square error defined over the parameters by generating a CLF matrix with appropriate elements. The performance and the applicability of the proposed scheme is illustrated through both simulations performed on a nonlinear system model and a real‐time laboratory experiment. Simulation study demonstrate the effectiveness of the proposed method in comparison with 2 other inverse control approaches. Finally, the proposed controller is implemented on a professional control board to stabilize a DC‐DC boost converter and minimize a meaningful cost function. The experimental results show the applicability and effectiveness of the proposed EKF‐based inverse optimal control even in real‐time control systems with a very short time constant.     

Adaptive rejection of unmatched input disturbances for output tracking using a control separation LQ method

In this paper, an adaptive disturbance rejection scheme is developed for output tracking of multivariable nonminimum‐phase systems in the presence of uncertain unmatched input disturbances. Using a new cost function, a control separation–based LQ control framework is established for desired disturbance rejection and output tracking. The finite‐time and infinite‐time control separation–based LQ solutions are derived in an explicit composite controller structure, which has enhanced disturbance compensation and output tracking properties, as compared with a traditional LQ solution. An adaptive parameter update algorithm is used for estimation of uncertain disturbances, based on which an adaptive control separation–based LQ control solution is developed for plants in the presence of uncertain disturbances. Simulation results are presented to verify the desired adaptive disturbance rejection control system performance.