DSP-Based Implementation of Fuzzy Output Tracking Control for a Boost Converter

Rotary inverted pendulum (RIP) system is a nonlinear, non-minimum phase, unstable and underactuated system. Controlling such system can be a challenge and is considered a benchmark in control theory problem. Prior to designing a controller, equations that represent the behaviour of the RIP system must be developed as accurately as possible without compromising the complexity of the equations. Through Takagi-Sugeno (T-S) fuzzy modeling technique, the nonlinear system model is then transformed into several local linear time-invariant models which are then blended together to reproduce, or approximate, the nonlinear system model within local region. A parallel distributed compensation (PDC) based fuzzy controller using linear quadratic regulator (LQR) technique is designed to control the RIP system. The results show that the designed controller able to balance the RIP system.

One of the common industrial structures that are used widely in many harbors and factories and buildings is overhead crane. Overhead cranes are usually operated manually or by some conventional control methods. In this paper, we propose a hybrid controller includes both position regulation and anti-swing control. According to Takagi-Sugeno fuzzy model of an overhead crane, a fuzzy controller designed with parallel distributed compensation and Linear Quadratic Regulation. With the Takagi-Sugeno fuzzy modeling, the nonlinear system is approximated by the combination of several linear subsystems in the corresponding fuzzy state space region. Then by constructing a linear quadratic regulation subcontroller according to each linear subsystem, a parallel distributed fuzzy LQR controller is designed. Further, the stability of the overhead crane with the parallel distributed fuzzy LQR controller is discussed. Simulation results illustrated the validity of the proposed control algorithm and it is compared with a similar method parallel distributed fuzzy controller.

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

In this paper, the issue of human behavior learning (HBL) is addressed for a class of nonlinear human-in-the-loop (HiTL) systems where the human operator is viewed as a nonlinear optimal controller. Owing to its outstanding interpretability and strong nonlinear representation capability, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear HiTL control system and approximate the unknown human control law based on the parallel distributed compensation (PDC) scheme. A quadratic-like cost function with fuzzy weighting matrices is built to depict the human behavior, which conforms to human thinking and is unknown to the machine. The aim of the HBL is to retrieve the fuzzy weighting matrices such that the human control law will be optimal in the sense of minimizing the retrieved cost function. In the proposed HBL scheme, the state-dependent Riccati equation (SDRE) based nonlinear optimal control technique plays an important role, which has a similar structure to the linear quadratic regulator (LQR) theory and thus is of low computational complexity. With the help of the PDC based fuzzy approximator for the unknown human control law, a two-step procedure is proposed for the HBL. First, a filter-based adaptive law is developed to learn the gain matrices of the fuzzy approximator using the system state data only. The convergence analysis of the adaptive estimator is also given. Then, a semidefinite programming (SDP) problem with the quadratic objective function can be set up for determining the fuzzy weighting matrices of the cost function. The simulation study on a steering control system of the intelligent vehicle is given to show the effectiveness and applicability of the developed approach.

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

This paper proposes an integral fuzzy control strategy to solve output regulation problem for the micro unmanned helicopter. In order to eliminate the system's bias and guarantee the zero-offset output regulation performance, we firstly take coordinate translation at equilibrium point and introduce an added integral state of output regulation error, and then the resulting augmented system is represented into a Takagi-Sugeno fuzzy model. Next, utilizing parallel distributed compensation (PDC) technique and direct Lyapunov method, an integral state feedback control law for output regulation is established by solving a set of linear matrix inequalities (LMIs). Moreover, the proposed controller design has following merits: i) capability to dealing with nonlinear affine system; ii) giving the exponential stability in the presence of model uncertainty; iii) possessing a piecewise constant output regulation performance. Finally, a micro unmanned helicopter dynamic model is presented to demonstrate the validity of the proposed integral fuzzy controller.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator (LQR) technique. The controller maintains the pendulum in the inverted (upright) position and is robust enough to reject external disturbance to maintain its stability. The research work involves three major contributions: mathematical modeling, simulation, and real-time implementation. To design a controller, mathematical modeling has been done by employing the Newton-Euler, Lagrange method. The resulting model was nonlinear so linearization was required, which has been done around a working point. For the estimation of the controller parameters, MATLAB LQR function has been utilized. Simulation has been performed for the designed controller and it also has been implemented and tested over the real inverted pendulum. From the results, it is vivid that the designed controller keeps the inverted pendulum in an upright position and rejects the disturbances and falling under gravitational force by adjusting the rotation of the horizontal link.

This paper addresses the issue of tracking the output of an activated sludge process using fuzzy integral control. First, the dynamics of the nonlinear process are modeled with a dynamic state space fuzzy model integrating the effect of external disturbances, and then an additional integral state of the output tracking error is introduced to obtain an augmented Takagi-Sugeno (TS) fuzzy model. The TS fuzzy model is able to describe the dynamics of complex nonlinear systems with an excellent degree of accuracy. It is formulated by fuzzy if-then rules which can give local linear representation of the overall nonlinear system. Second, the design of the fuzzy integral control is performed, in which the state feedback gains are obtained by solving linear matrix inequalities (LMI). The objective is to ensure trajectory tracking of an activated sludge process (ASP) by controlling two key variables: the substrate concentration and the level of dissolved oxygen. To assess the performance of the proposed control strategy, a comparative analysis is carried out with a gain scheduling PI (GS-PI) controller. Simulation results are provided to illustrate the effectiveness of the proposed approach. Where, the fuzzy integral control reduces the high energy consumption in water treatment plants.

Robotic manipulators are widely used in applications that require fast and precise motion. Such devices, however, are prompt to nonlinear control issues due to the flexibility in joints and the friction in the motors within the dynamics of their rigid part. To address these issues, the Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) approaches are implemented in the Takagy-Sugeno Fuzzy Model (T-SFM). We propose the following methodology; initially, the state space equations of the nonlinear manipulator model are derived. Next, a Takagy-Sugeno Fuzzy Model (T-SFM) technique is used for linearizing the state space equations of the nonlinear manipulator. The T-SFM controller is developed using the Parallel Distributed Compensation (PDC) method. The prime concept of the designed controller is to compensate for all the fuzzy rules. Furthermore, the Linear Matrix Inequalities (LMIs) are applied to generate adequate cases to ensure stability and control. Convex programming methods are applied to solve the developed LMIs problems. Simulations developed for the proposed model show that the proposed controller stabilized the system with zero tracking error in less than 1.5 s.

This paper proposes a design method of H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> control performance for structural systems using Takagi-Sugeno (T-S) fuzzy model. The structural system with tuned mass damper is modeled by T-S type fuzzy model. By using parallel distributed compensation (PDC) scheme, we design a nonlinear fuzzy controller for the tuned mass damper system. According to the control system, a sufficient stability condition is derived in terms of Lyapunov theory and this control problem is reformulated into solving linear matrix inequalities (LMI) problem.

This paper presents a trajectory tracking control approach for a mobile robot in the presence of static obstacles on the reference trajectory. The tracking control is developed based on the fuzzy parallel distributed compensation scheme where the linear quadratic regulator is used as a state feedback controller for each subsystem. The obstacle avoidance task is accomplished by applying a linear quadratic regulator on the overall open loop Takagi-Sugeno (T-S) fuzzy system, in which the weighting matrices are adjusted dynamically using a fuzzy controller. A fuzzy fusion controller is designed to combine the tracking and the obstacle avoidance velocities in order to perform both tasks simultaneously. Simulation results illustrate the effectiveness of the proposed control strategy.

This paper addresses the design of fuzzy state feedback controller that has not only the ability to stabilize the fuzzy model/system but also to control the transient behaviour and closed loop pole location for wind energy conversion system which present interesting control demands and exhibits intrinsic non-linear characteristics. The proposed fuzzy controller is employed to regulate indirectly the power flow in the DC link by regulating the DC current. First, a Takagi-Sugeno fuzzy model is employed to represent a non-linear system. Then a model-based fuzzy controller design utilizing the concept of parallel-distributed compensation is developed. Additional constraints on the closed loop pole location are satisfied. Satisfactory time response and closed loop damping are achieved by forcing the closed loop poles into a suitable sub-region of the left half plane. These conditions are expressed in terms of linear matrix inequalities (LMI's), which can be solved very efficiently using convex optimization techniques. The design techniques are applied to a dynamic model of wind energy conversion system to illustrate the feasibility of the proposed solution.