The error signal is yout, the output computed by calling sim, minus the input signal 1. This is defined via a MATLAB function in the file tracklsq.m, shown below, that defines the error signal. The routine lsqnonlin is used to perform a least-squares fit on the tracking of the output. But the goal is to minimize the error for all time steps from 0 to 100, thus producing a multiobjective function (one function for each time step). If you only need to minimize the error at one time unit, it would be a single objective function.
The variables are the parameters of the PID controller. One way to solve this problem is to minimize the error between the output and the input signal. A Scope block displays output trajectories during the design process. The closed-loop plant is entered in terms of the blocks where the plant and actuator have been placed in a hierarchical Subsystem block. The problem is to design a feedback control loop that tracks a unit step input to the system. You can see this response by opening the model (type optsim at the command line or click the model name), and selecting Start from the Simulation menu. The open-loop response of the system to a step input is shown in Figure 2-2, Closed-Loop Response. The slew rate limit of the actuator is 0.8 units/sec. The actuator saturation limit cuts off input values greater than 2 units or less than -2 units. The actuator limits are a saturation limit and a slew rate limit. The plant is an under-damped third-order model with actuator limits. Note that Simulink must be installed on your system to load this model.) The model includes a nonlinear process plant modeled as a Simulink block diagram shown in Figure 2-1, Plant with Actuator Saturation.įigure 2-1: Plant with Actuator Saturation (This model can be found in the Optimization Toolbox optim directory. Let's say that you want to optimize the control parameters in the Simulink model optsim.mdl.
#Matlab optimization toolbox multiple design variables how to#
Included is an example of how to optimize parameters in a Simulink model. This section demonstrates solving problems with multiobjective functions using lsqnonlin, fminimax, and fgoalattain. The previous examples involved problems with a single objective function. It enables you to find optimal solutions in applications such as portfolio optimization, energy management and trading, and production planning.Tutorial (Optimization Toolbox) Optimization Toolbox The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. You can use the toolbox solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications. You can use automatic differentiation of objective and constraint functions for faster and more accurate solutions.
You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics. The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming (QP), second-order cone programming (SOCP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints.
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